Here's the background to the case, in the words of SCOTUSblog:
"As part of its lethal injection protocol for executions, Oklahoma uses a sedative called midazolam, which is used to treat anxiety, to make the inmate unconscious. Two other drugs then paralyze him and stop his heart. A group of Oklahoma death-row inmates have challenged the state's use of midazolam, arguing that it cannot reliably render an inmate unconscious.
"The difference between midazolam and other drugs (like pentobarbitol) is that it's not a barbiturate. So the inmates' argument was that it wouldn't cause the sort of deep coma that would prevent pain later in the execution procedure." Read more...
MAP: Lethal Injection By Far The Most Popular Execution Method In U.S. : It's All Politics : NPR
States may continue using a popular but controversial drug in lethal injection executions, the Supreme Court ruled on Monday in a 5-4 decision. In Glossip et al. v. Gross et al., the question was whether or not to allow states to use midazolam, a drug used to render inmates unconscious before executing them. The April 2014 execution of Clayton Lockett in Oklahoma helped bring the topic to public attention. In that case, high doses of midazolam failed to sedate Lockett sufficiently, and he yelled in pain while the other execution drugs were administered. In today's case inmates in Oklahoma filed a petition with the court, saying the use of midazolam violates the eighth amendment to the Constitution, which protects against the use of cruel and unusual punishment. Today, lethal injection is by far the most popular method of execution in US states, with all 31 states that authorize the death penalty using it, and many of those states have been using midazolam, as NPR's Nina Totenberg reported in April.
Lethal Injection Is Used In Every Death Penalty State
Death penalty legal in any form
Notes— New Mexico and Connecticut have abolished the death penalty, but their laws were not retroactive so inmates remain on death row.
— New Hampshire authorizes hanging only if lethal injection is unavailable.
— In Oklahoma electrocution may be used if both lethal injection and nitrogen gas are found unconstitutional. The firing squad may be used if electrocution is also found unconstitutional.
— In Tennesee electrocution may be used if lethal injection drugs are unavailable.
— In Utah, the firing squad may be used if lethal injection is found unconstitutional.