Washington (CNN) A full-strength Supreme Court will take the bench Monday for what could be the most consequential term in decades, as the ideologically split justices consider cases as diverse as religious liberty, immigration, cell phone privacy, voting rights and possibly the legality of President Donald Trump's controversial travel ban.

"There is only one prediction that is entirely safe about the upcoming term, and that is it will be momentous," Justice Ruth Bader Ginsburg said at an event at Georgetown Law recently.

The justices spent most of last term with only eight members rendering narrow opinions -- at times -- in an attempt to ward off 4-4 splits.

But that's all over now.

Justice Neil Gorsuch has settled into his new role as a staunch conservative, filling the role previously held by the late Justice Antonin Scalia.

That means there are five conservatives and four liberals on the bench, with Justice Anthony Kennedy resuming his post as the swing vote from the conservative- to liberal-leaning side. Sources say he has been seriously considering retiring, and liberals fear that their last remaining chance at a win on issues -- like LGBT rights -- might rest with him.

Here are the big issues this year:

Travel ban

Leading the docket, until recently, was a challenge to Trump's signature policy: the travel ban. The justices were scheduled next week to hear oral arguments and decide whether the President was legally justified when he temporarily blocked travel from several Muslim-majority countries, citing national security concerns.

Challengers argue that the executive order violates the the Constitution. They say the President was motivated in part by religious animus and point to some of the things Trump said during the campaign calling for a Muslim ban.

"The President has claimed limitless authority to exclude any alien he wishes," Neal Katyal, the lead lawyer for Hawaii, wrote. "This court has the power and the duty to police these excesses."

But the administration says the White House has the authority to act to restrict immigration.

"The Constitution and Acts of Congress confer on the President broad authority to suspend or restrict the entry of aliens outside the United States, when he deems it in the Nation's interest," Acting Solicitor General Jeffrey Wall wrote in court papers.

Late last spring the justices allowed part of the travel ban to go into effect, pending appeal, for foreign nationals who "lack any bona fide relationship with any person or entity in the United States." They were scheduled to hear oral arguments October 10 -- but that's now been postponed

The twist: Last month, the President replaced a major provision of his controversial March executive order with new restrictions that have yet to go before any court.

Now, the justices must decide whether they should hear the challenge, or send the case back down to the lower courts to take a fresh look.

JUST WATCHED Trump's latest travel ban Replay More Videos ... MUST WATCH Trump's latest travel ban 01:31

Immigration

The court this week will rehear two immigration-related cases will be watched closely for tea leaves of what justices are thinking on the travel ban, although they don't pertain to it specifically.

Monday, the court will rehear a case concerning mandatory deportation of lawful permanent residents for criminal convictions.

The Sessions v. Dimaya case was argued before the court in January, before Gorsuch was nominated and confirmed. At the end of June, the justices signaled they were divided 4-4 on at least some aspects of the case and wanted Gorsuch to weigh in.

Tuesday, justices rehear another immigration related case, Jennings v. Rodriguez. The case was brought by a class of immigrants -- some who sought entrance at the border, others lawful permanent residents -- who are fighting removal and arguing that they cannot be held in prolonged detention. After six months of detention, they seek hearings to prove that they are neither a flight risk nor a danger to society.

"Both cases implicate the scope of the government's authority over different classes of immigrants in ways that won't directly bear on the travel ban litigation, but could provide important clues into what the key justices are thinking," said CNN legal analyst and University of Texas Law School professor Steve Vladeck.

Voting rights and gerrymandering

Tuesday, justices will tackle a case that could reshape electoral maps across the country.

At issue is partisan gerrymandering -- or the length to which legislators go when they manipulate district lines for partisan advantage. Democratic voters in Wisconsin are challenging maps they say were drawn unconstitutionally to benefit Republicans.

While the Supreme Court has a standard limiting the overreliance on race in map drawing except under the most limited circumstances, it has never been successful in developing a test concerning the overreliance on politics.

Wisconsin, in its arguments, says that both the challengers have no power to bring such a claim and that the issue should be decided not by the judiciary but the political branches.

Redistricting is an issue close to former President Barack Obama, who has vowed to dedicate part of his post-presidency to the issue. Prominent Republicans such as Arizona Sen. John McCain and former California Gov. Arnold Schwarzenegger have filed briefs in support of the challengers, arguing that the issue does not only adversely impact Democrats.

"It's not a Democratic or a Republican issue," Schwarzenegger said in a recent conference call," it's simply a power issue."

Another election law case, Husted v. Randolph Institute, will be heard in early November dealing with Ohio's method of removing names from its voter rolls. A federal appeals court ruled that the program violates the National Voter Registration Act.

Religious liberty

One of the most controversial cases of the term pits claims of religious liberty against LGBT rights.

At the center of the case is Jack Phillips , who owns a bakery called Masterpiece Cakeshop in Colorado. In 2012, he refused to make a cake to honor a couple's same-sex marriage, citing his religious beliefs. Lower courts ruled in favor of the couple, citing a state anti -discrimination law.

Now Phillips, who calls himself a "cake artist," is asking the Supreme Court to protect his rights, and he received a big boost last month from the Trump administration.

"Forcing Phillips to create expression for and participate in a ceremony that violates his sincerely held religious beliefs invades his First Amendment rights," acting Solicitor General Jeff Wall wrote for the Justice Department in briefs filed to the court.

"The government may not enact content-based laws commanding a speaker to engage in protected expression: An artist cannot be forced to paint, a musician cannot be forced to play, and a poet cannot be forced to write," Wall added.

Louise Melling, an ACLU lawyer representing the plaintiffs, says that the Masterpiece case is "making a radical argument."

"When you look at it, they are saying there is a constitutional right, whether it's rooted in speech or religion, to discriminate," she said in an recent interview.

"A ruling for the bakery would have implications far beyond LGBT people and would put in jeopardy our longstanding laws against discrimination," she said.

JUST WATCHED Wedding cake leads to Supreme Court case Replay More Videos ... MUST WATCH Wedding cake leads to Supreme Court case 01:08

Cell phone privacy

The court will also hear a major case concerning privacy in the digital age when it determines whether investigators need to obtain a warrant for cell tower data to track and reconstruct location and movements of cell phone users over extended periods of time.

The case was brought by the ACLU on behalf of two men who were arrested after a string of robberies in Michigan and Ohio. At trial, the government's evidence included records from the defendants' phones that showed that the men used their phones within a close radius to several robberies.

How the justices decide the issue could provide a framework for other issues such as facial recognition technology and surveillance law.

Most courts have held that there is a diminished privacy interest in this area because the information has already been provided to third parties such as phone companies.