The Supreme Court this month began hearings on oral arguments in a slew of cases that could have serious implications for state and local governments.

Among the biggest cases during the court's latest term are ones that deal with affirmative action and prayer at government meetings.

All total, the court is scheduled to hear oral arguments in more than three dozen cases through December. Here's a breakdown of which ones could have the biggest impact on Governing readers.

Town of Greece, N.Y. v. Galloway: The town invites residents of any religion -- or no religion -- to deliver an invocation before its public meetings. In practice, just four of those prayers have been led by non-Christians. The court will have to determine whether the town has violated the the Constitution's Establishment Clause in allowing those prayers. A federal appeals court found Greece in violation of the Establishment Clause and struck down the Town's prayer practice.

ScotusBlog writes that the case is a surprising one for the court to take up. "The Town of Greece, a suburb of Rochester, New York, has a population of about 100,000, and the case seemed to have no national importance before the Supreme Court accepted it for review," it wrote. "Indeed, commentators are still surprised that the Obama administration even weighed in on it." U.S. Solicitor General Donald Verrilli wrote an amicus brief supporting the town.

The court previously ruled in 1983 that state legislatures could have chaplains offer prayers if they didn't advance or disparage any faith. The re-visitation of the issue could have implications for governments that begin their sessions with prayer.

Schuette v. Coalition to Defend Affirmative Action: The case is a response to a voter-approved 2006 referendum to amend Michigan's constitution. Voters opted to ban "preferential treatment to any individual or group on the basis of race" in an effort to ban affirmative action in the university admissions process. But a federal appeals court last year ruled that the law was unconstitutional and undermined the rights of minorities. Michigan Attorney General Bill Schuette is arguing to put the language back on the books.

The question before the court is whether a state violates the Equal Protection Clause of the U.S. Constitution by prohibiting race and sex based discrimination or preferential treatment in the college admissions process. Interestingly, a similar case last term, Fisher v. University of Texas at Austin, asked the mirror  image of that question: whether affirmative action policies themselves were a violation of the Equal Protection Clause. It tightened up some of the parameters for affirmative action, but it didn't make a sweeping ruling. If the court makes clear through Schuette that states may ban affirmative action, that could have huge implications and may cause others to follow Michigan's lead.

Madigan v. Levin: The case concerns Harvey Levin, an attorney for the state of Illinois who accused the state of age discrimination for firing him at 61 and hiring a younger attorney. He filed a lawsuit, but the question is whether people in his position can take their case straight to the courts or must first follow administrative procedures set forth in the federal Age Discrimination in Employment Act . A circuit court said Levin could file his suit, but Illinois Attorney General Lisa Madigan argues that age discrimination allegations must first go through the EEOC, as outlined in ADEA.

Employers, including state and local governments, have a stake in the case, since litigation is typically more costly than resolving the issue before the courts get involved.

On Tuesday, the court made its first ruling of the term, and it wasn't an exciting one: justices decided they shouldn't have taken up the case.

Environmental Protection Agency v. EME Homer City Generation: The case revolves around the question of just how much authority the EPA has to regulate states whose air pollution is impacting other states downwind. The debate is over a rule that largely addresses smokestack pollution from power plants, which can drift for hundreds of miles, according to the Environmental Defense Fund.

The Supreme Court took up the case after an federal appeals court invalidated a 2011 EPA rule designed to address cross-state air pollution. As Reuters, in a lengthy analysis of the case wrote:

The rule sets limits on nitrogen oxides and sulfur dioxide from coal-fired power plants in 28 upwind states in the eastern part of the country. Various power companies and 16 states successfully challenged the law in the U.S. Court of Appeals for the District of Columbia Circuit. The appeals court ruled 2-1 in August that the EPA had exceeded its authority under the Clean Air Act by requiring states to curb air pollution to a greater extent than the (Clean Air Act) requires.

One of the questions the court could answer is whether or not EPA should consider the cost of reducing air pollution as part of states' plans to reduce harmful pollutants. It could also answer whether states can avoid developing "state implementation plans" that prohibit certain types of emissions until EPA has adopted another rule that further quantifies each state's obligations.

Almost all of the states have weighed in on the debate, largely based on whether they're upwind states or downwind states, says Lisa Soronen, executive director of the State and Local Legal Center.

McCutcheon v. FEC: The case is being brought by Shaun McCutcheon, a conservative Alabama businessman seeking to remove certain limits on federal campaign contributions.Though the case revolves around federal campaign contribution limits, there may be impacts on states too.

Soronen says about a dozen states have their own aggregate campaign contribution limits. Observers say the ruling could have the most significant impact on campaign finance law since the famous Citizens United ruling in 2010, which banned restrictions on independent expenditures.

McCullen v. Coakley: The court will consider a challenge to a Massachusetts law that creates a 35-foot "buffer zone" around abortion clinics that protesters are barred from entering. The petitioners, who do "pro-life counseling" outside abortion clinics, argue the law is a classic First Amendment Violation, but so far, lower federal courts have taken the state's side and upheld the law. A 2008 Supreme Court case upheld a similar Colorado law as well.

Soronen says buffer zones "are king of more common than you think," with some places having buffer zones around ATMs designed to prevent panhandling or around city hall for political demonstrations. If the Massachusetts law is struck down, other jurisdictions may need to rewrite their buffer zone laws.