The Supreme Court ruled largely in favor of the U.S. on Arizona's immigration law, but it upheld the most controversial provision involving police checks on people's immigration status.

So what did we learn and what can we glean from their decision? Bill Mears, CNN's Supreme Court producer, breaks down the decision piece by piece:

1. Others states better tread carefully

By striking down three of the four major provisions and upholding the idea of federal authority on this issue in pretty sweeping comments, the Supreme Court has signaled other states with similar laws that they better tread carefully or make sure their laws do not to reach too far.

In Justice Anthony Kennedy's majority opinion, his main point was that the national government has significant power to regulate immigration issues. And so that lets states know that while they have some place to play in the issue, the federal government still reigns supreme.

While the court didn’t tell Arizona and other states what they could and couldn’t do when they conduct a traffic stop - for example how long police can hold someone, whether the law would amount to racial profiling - this opinion is essentially guidance moving forward. Their opinion was certainly not a complete smackdown of Arizona's law. Instead, it left some things pretty ambiguous.

2. The one provision upheld could be challenged again

The provision that was upheld by all eight ruling justices - commonly called the "show me your papers" provision - allows local law enforcement, when performing other state law enforcement functions, to check on the immigration status of those people they stop for another reason. That part was upheld because the justices said it was complementing existing federal policy. That's as long as police weren’t singling people out specifically for racial reasons. The court essentially said that if police stop someone properly, or are involved in a domestic dispute, it was perfectly proper to at least check an immigration status and then consult with federal officials.

But in upholding that provision, the court was very careful to say that depending on how this is implemented, it could very well be overturned one day. The overall lawsuit brought against the law is a facial challenge, which means it was being opposed and believed to be unconstitutional before it went into effect. What the court is saying when it comes to the "show me your papers provision" is that the justices are going to uphold it for now, allow Arizona to implement it and depending on how they enforce it, deal with it later.

If in the future a challenge is brought claiming that people are being detained for an extended time or racial profiling is occurring, it could be challenged in the state and federal courts again, now that it can actually be implemented as a law. The justices have essentially said they will give Arizona the benefit of the doubt that they will enforce this in a way that meets a constitutional muster test.

It’s a signal to other states that if they are going to have similar provisions, they too have to be careful.

3. Both sides can claim victory - and they'll be right

Both sides can claim victory in this case, maybe not legally, but from a political point of view. The Supreme Court has in a way given both sides rightful reasons to claim they have won.

Many states will be encouraged by upholding a key provision dealing with "show me your papers" and that may be an impetus for states to go ahead and move forward with their legislation. After all, by upholding that, it says that states do have some kind of role in the matter, they just have to avoid overstepping federal authority.

For the Obama administration and opponents of the Arizona law, they will be able to say that almost all of that state law was thrown out by the Supreme Court and federal authority remains supreme.

It is really more about political rhetoric and both sides saving face.

The justices know the law is nuanced. They don’t want to try to dictate from the bench or tell states or the government how to do their business. They’ve given the benefit of the doubt to all sides to work this out.

Sometimes that frustrates people because they want the clear and unequivocal answer from the Supreme Court, but the justices try to do that sparingly. When they can do as little as possible and still satisfy the U.S. Constitution, that is usually what they will try to do. They're very sensitive to being seen as legislating from the bench and really like to only step in and make sweeping opinions when an issue has gone too far. In this case, they've laid down the framework for both sides to work toward forming a practical and political standpoint.

4. Will this have implications for the presidential election?

While there is a lot of chatter right now about immigration, it isn't likely to be a huge national issue when it comes to November. Each state has its own policy, and for those that have their plans on hold because of the Supreme Court challenge, it will take probably a year to sort all of that out. It’s a question of timing. By the time the courts sort out which states and which policies are proper, it may very well be past Election Day.

Polls also continue to show that Americans don’t think what the Supreme Court does is as important as the economy. And they always rank near the bottom when it comes to what issues that are important. There's likely not much political mileage out of it.

Can the candidates make it into a larger issue?

For Obama and presumptive GOP nominee Mitt Romney, it might be one they take to a swing state or somewhere deeply affected by immigration such as Texas, Arizona and California, but it's hard to see it becoming a national strategy for a talking point. They may incorporate the effect illegal immigration has on the economy into their speeches, but that’s not going to be a key selling point. And there isn't as much voter angst about the issue as others.

5. Can we glean anything from this ruling, looking ahead to health care?

One of the first things you might have noticed about the opinion was that Justice Kennedy and Chief Justice John Roberts came down on the same side as the liberal side of the bench. It makes you wonder: What does it mean for health care?

Some people in the legal spheres have suggested that the chief justice's support for striking down most of Arizona’s law was curious and wondered whether it suggested something else was happening behind the scenes.

While some quipped that perhaps a vote for immigration was traded for health care, the justices don’t horse trade on those kinds of things. But it may signal their mind-set – an agreement when it comes to federal authority. Roberts has talked about respecting other branches even when it conflicts with state power in recent years.

And if there's one nexus between health care and immigration, it’s the issue of federal authority.

If you believe what the majority justices are saying in Monday's Arizona ruling, the federal government in a lot of areas has supremacy.

And that certainly has legal scholars on both sides wagging their tongues about whether Kennedy and Roberts might feel strongly enough about federal power that they could be persuaded to uphold the Affordable Care Act on health care in a very, very narrow ruling.

The question really remains: If Kennedy and Roberts affirmed federal supremacy for immigration, will they rule the same way for Congress on health care?