Here's a look at some of the most consequential issues.
Shortly after Mr Kennedy announced his retirement, Supreme Court analyst Jeffrey Toobin tweeted that "abortion will be illegal in 20 states in 18 months" - an indication that he believes Mr Trump's nominee will join a majority in reversing Roe v Wade, the 1971 decision legalising abortion throughout the US.
Anti-abortion advocates have been trying to scale back the broad constitutional guarantees of the Roe decision in the decades since, and now - without Mr Kennedy on the court - they could be poised for a breakthrough.
Back in 1992, when Mr Kennedy was just a junior justice, the court considered a series of Pennsylvania restrictions on abortion rights in a case, Planned Parenthood v Casey, that could have drastically curtailed what had been established as a constitutional right to abortion.
Mr Kennedy reportedly initially sided with the more conservative justices but eventually co-wrote a three-justice plurality that upheld the "essential holding" of the landmark Roe decision legalising first-trimester abortions throughout the US.
Since then, Mr Kennedy has frequently sided with abortion rights advocates in the court, most recently last year, when he joined the court's four liberal justices to strike down a Texas law stringently regulating abortion clinics and the doctors who perform the procedure.
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