More challenges to Obamacare making their way through the courts

The U.S. Supreme Court on Thursday upheld tax subsidies crucial to President Barack Obama's healthcare law, but several other challenges to the 2010 statute are making their way up through the courts.

Here is a look at some of the major cases and the grounds on which they have been brought.

U.S. House of Representatives v. Burwell

Filed last November by House Republicans, the lawsuit challenges the Obama administration's implementation of the Affordable Care Act, widely known as Obamacare. The lawsuit claims some of the administration's actions to put the law into effect required, but did not receive, congressional authorization. Those actions included delaying implementation of a mandate that certain employers buy insurance for their employees and authorizing the Treasury to make payments to health insurers without getting funding from Congress. The administration's motion to dismiss the case is pending before the U.S. District Court for the District of Columbia.

Sissel v. U.S. Department of Health and Human Services (HHS), Hotze v. Burwell

These lawsuits assert that the law, which originated in the Senate, violates the Constitution's "origination clause," which requires a bill raising revenue to originate in the House. In 2012, the Supreme Court said the penalty on individuals for failing to buy health insurance could be regarded as a tax. The Sissel lawsuit was rejected last July by the D.C. Circuit Court of Appeals, which found the "origination clause" did not apply because raising revenue was incidental to the main purpose of the law. The plaintiff, an artist who sells his work out of his studio, is asking for a rehearing. The other case, Hotze v. Burwell, was dismissed by the 5th Circuit Court of Appeals in April for lack of standing. The plaintiff, a Texas doctor, is also seeking a rehearing.

Michigan Catholic Conference v. Burwell and other lawsuits challenging the contraception mandate and related waiver

In a series of cases, non-profit employers have objected to the process for opting out on religious grounds of the law's requirement to buy contraception coverage for their employees. Such employers must provide a form to their insurers, which then separately must provide contraception coverage for employees. Numerous employers have claimed in lawsuits that submitting the form goes against their religious objections. One of the most closely watched is Michigan Catholic Conference v. Burwell, which was dismissed by the 6th Circuit U.S. Court of Appeals last June. The plaintiffs, a group of Catholic employers, are asking the Supreme Court to take the case. Another is Zubik v. HHS, which was brought by Pittsburgh Catholic bishop David Zubik. Though the 3rd Circuit U.S. Court of Appeals dismissed Zubik's case in 2013, Supreme Court Justice Samuel Alito put that decision on hold in April pending further review.