Washington (CNN) The Supreme Court is entering the final rounds of a term featuring a newly solidified conservative majority that has faced off at times against the four liberal justices and seen some dramatic moments.

So far, Chief Justice John Roberts has bobbed and weaved, balancing his institutional concerns against his own solidly conservative leanings. Justice Brett Kavanaugh joined the court in the early part of the 2018-19 term after a contentious nomination hearing featuring allegations of sexual misconduct as a teenager (he has denied the allegations). Justice Ruth Bader Ginsburg had two cancerous nodules removed from her left lung in December.

There have been some opinions that resemble compromises.

Neither Elena Kagan nor Stephen Breyer publicly dissented when the court issued an unsigned opinion allowing one provision of an Indiana law go into effect that mandated the burial or cremation of fetal remains. On the same day, the justices left in place a lower court ruling that invalidated a much more restrictive abortion related provision of the same law. Justice Clarence Thomas, kept up the pressure from the right side of the bench reminding his colleagues of his view that "the Constitution itself is silent on abortion."

The justices have met week after week and extended courtesies on the bench such as Thomas silently offering a hand to Ginsburg as she leaves the courtroom, but they've also feuded late into the night on death penalty petitions.

As the term ends the country will see where they stand on a citizenship question on the 2020 census, as well as the issue of extreme partisan gerrymandering. And all eyes will look to next term -- held in the heat of the election—to see which cases the court will decide to hear.

Here's a look at the key remaining opinions:

2020 Census citizenship question (Dept. of Commerce v. New York)

The Supreme Court is wading into a bitter controversy over whether the Trump administration can ask all recipients a citizenship question on the 2020 census for the first time since 1950.

The administration claims that the question is necessary to better comply with federal voting rights law, while critics say it represents a veiled attempt to intimidate noncitizens and Hispanic households and will lead to a decrease in response rates.

Every lower court to consider the issue has so far blocked the administration from adding a question about citizenship status to the census questionnaire, holding that Commerce Secretary Wilbur Ross, who has jurisdiction, exceeded his authority under federal law or the Constitution by doing so. After arguments, the challengers informed the court they had obtained "new evidence" that the decision was politically motivated.

Why it matters: With the 2020 census fast approaching, how the justices rule in this case about political representation could impact the critical data derived from the census, which is used for issues such as the allocation of congressional seats and the distribution of billions of federal dollars to states and localities over the next decade.

Partisan gerrymandering (Rucho v. Common Cause and Lamone v. Benisek)

The court is considering when politicians go too far in drawing lines for partisan gain , in a set of cases arising from North Carolina and Maryland that could fundamentally impact the balance of power in legislatures and Congress. Similar cases out of Ohio and Michigan have been put on hold pending the Supreme Court's decision.

Although the court has a standard to weed out extreme racial gerrymanders, it has never been able to settle on a standard for partisan gerrymandering.

With the retirement of Justice Anthony Kennedy, critics of extreme partisan gerrymandering fear they may have lost the last chance at a meaningful test.

They say that with sophisticated new redistricting technology, map drawers are able to manipulate the system more than ever, and entrench the governing party in power. States argue that there is no manageable standard and that the Constitution gives them broad authority to regulate redistricting.

The North Carolina case is brought by Democrats challenging Republican-drawn districts, the Maryland case is Republicans challenging a Democratic district. The lower courts struck the districts and provided the justices with several potential tests grounded in the First Amendment, the Equal Protection Clause and other parts of the Constitution to establish a new standard.

Why it matters: On the eve of the next census, this case could change how maps are drawn. The justices could, for the first time, establish a test to determine when partisan motivation is too much, or they could slam the door shut on such claims, holding that it is an issue better left to the political branches of government.

Racial gerrymandering (Virginia House of Delegates v. Bethune Hill)

The court is looking at 11 districts drawn by the Republican-led legislature in Virginia in 2011 that were struck down as an unconstitutional racial gerrymander by the lower court.

Registered voters in each district challenged the maps and prevailed below when a lower court held that they had "shown through telling direct and circumstantial evidence that race predominated over traditional districting factors."

Lawyers for Virginia's House of Delegates are seeking to represent the state over the objections of the Democratic governor and attorney general and they are asking the Supreme Court to reverse the lower court. They say the maps were drawn to comply with the Voting Rights Act.

Two questions are before the justices: Does the House of Delegates have the legal right, or "standing" to bring the challenge, and should the districts be struck down as an unconstitutional racial gerrymander.

Why it matters: These districts will only be used for the off year election and 2020, whoever wins will draw the new districts after the next census.

Maryland 'Peace Cross' (American Legion v. American Humanist)

The American Legion built the so-called "Peace Cross" in 1925 to honor 49 local men who died serving in World War I. Mothers of the fallen soldiers designed the memorial to mirror the crosses that mark graves in American cemeteries overseas.

The cross was deeded to the Maryland-National Capital Park and Planning Commission in 1961, after a highway was built around it. It stood without conflict until 2012, when nearby residents sued, arguing that they are offended by the government's endorsement of religion and the fact that the cross is maintained with taxpayer money.

The Trump administration supported the American Legion and urged the justices to take a historical approach to the case.

Why it matters: After oral arguments it seemed like the justices were going to rule in favor of the cross. But will the ruling be narrow only covering war memorials that stand in public parks, or could the court go farther to allow more religion in the public sphere instances like holiday displays, prayer at public meetings, "in God We Trust" on coins?

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Race in jury selection (Flowers v. Mississippi)

Curtis Flowers, an African-American on death row, was tried five times for the 1996 murder of four people inside a furniture store in Winona, Mississippi. But it was only in 2010, after his sixth trial, that a conviction stuck and Flowers was sentenced to death.

Now, his lawyers want his conviction reversed. They want justices to hold that Flower's rights were violated by the prosecutor, Doug Evans, who they say engaged in race discrimination during jury selection. During oral arguments -- where Justice Clarence Thomas asked a rare question -- the justices seemed ready to rule in favor of Flowers. The question will be how broad the ruling will be.

Why it matters: Supporters of Flowers say the Supreme Court needs to add teeth to the decision -- called Batson v. Kentucky --because prosecutors can get around it by simply supplying race neutral justifications while building mostly white juries.

First Amendment patent claims (Iancu v. Brunetti)

Entrepreneur Erik Brunetti says he founded a clothing brand -- called FUCT -- in 1990 to question authority and the assumptions of society. On the way, he also triggered a First Amendment dispute that has landed at the highest court in the land.

Brunetti says, his company's name stands for FRIENDS U CAN'T TRUST. In 2011, he sought to register the mark with the United States Patent and Trademark Office in order to obtain benefits such as expanding rights against others attempting to use the same mark.

But the office did not buy Brunetti's explanation for the meaning of FUCT. Instead, it said the word was the "phonetic equivalent" of the past tense of a vulgar word. It refused Brunetti's request determining that federal law prohibits the registration of trademarks that consist of "scandalous" subject matter.

Now the Supreme Court, for the second time in two years, will review whether provisions of a federal law, the Lanham Act violate the First Amendment.

Why it matters: If the justices rule in favor of Brunetti, they could open the doors to more so-called "scandalous" marks in the marketplace and even broaden a category of speech protected by the Constitution. At oral argument, however, they seemed to suggest that they might uphold the statute as it applied to some really offensive words.

Indian territory jurisdiction (Carpenter v. Murphy)

Patrick Murphy, a member of the Creek Nation, was convicted of murdering a fellow tribe member, George Jacobs, and sentenced to death by Oklahoma in 2000.

But Murphy argued he was tried in the wrong court. He said his crime occurred on Indian territory, and that the federal government, not the state, had jurisdiction.

His case raises a question that could have broad repercussions and could impact at a minimum 2,000 other prisoners in state court and self-identify as Native American.

The 10th US Circuit Court of Appeals ruled in Murphy's favor holding that the state lacked the jurisdiction because Congress had never "disestablished" the 1866 boundaries of the Creek nation that encompasses 3,079,095 acres. Currently 1.8 million Oklahomans live on the land.

Under federal law, major crimes committed by Indians on Indian country must be tried in federal court.

Murphy's death penalty case opened a hornet's nest for the court. Lisa Blatt, a lawyer for Oklahoma, warned if the Supreme Court were to uphold the lower court opinion it would be a blow to the State's power to prosecute and burden federal authorities forcing them to investigate and prosecute hundreds of new cases each year.

Justice Neil Gorsuch recused himself from the case as he dealt with the case previously when it came before the 10th Circuit.

Why it matters: if the court were to affirm the lower court the government says it would impact pending and past convictions and broaden the government's authority.

Double Jeopardy (Gamble v. United States)

The Double Jeopardy clause to the Fifth Amendment prohibits more than one prosecution for the same offense. There is an exception, however, that is called the "separate sovereigns exception."

Under the exception, prosecutions are allowed to bring charges for the same offense if the charges are brought by state and federal government. The Supreme Court is being asked to get rid separate sovereigns exception.

Critics contend that in the modern day it leads to harassment of defendants -- especially the poor -- who can't afford to fight on two fronts.

The case could impact President Donald Trump's pardon power as it applies to the Robert Mueller probe. The thinking goes that if he pardoned someone like Paul Manafort, then state officials could not bring the same charge against him. Others say that it would have no impact because state prosecutors would be savvy enough to bring charges for a different offense.

The Trump administration argued that the exception should remain on the books.

Why it matters:

On one hand, the federal government and others say this exception is meant to protect the independent power of state and federal governments. It has been a part of the court's fabric for more than 150 years.

Veteran disability benefits (Kisor v. Wilkie)

At issue is a dispute between Marine veteran James L. Kisor, who is seeking disability benefits for his service-related post-traumatic stress disorder, and the Department of Veterans Affairs that had declined to award him retroactive benefits.

But lurking behind the case is a much bigger legal dispute over whether courts should defer to an agency's interpretation of its own regulations when there is ambiguity. In legalese it's called "Auer deference."

Why it matters: Conservatives -- like former White House Counsel Don McGahn, who attended oral arguments -- argue that agencies have become too powerful, upsetting the balance of power. But progressives argue that agency deference is important for the regulation of big business and the protection of consumers, the environment and workers.