The US Supreme Court has a huge impact on American social policy and political life and the appointment of a new judge to the court is seen as a key moment in any presidency.
As the highest court in the land and the final interpreter of the US constitution, its rulings have been decisive on such issues as abortion, civil rights and the death penalty.
With the nine judges each appointed for life, the choice of a new justice potentially gives a president an opportunity to help shape its decisions for years to come.
Established in 1789 under Article III of the constitution, the court may hear about a hundred cases a year - mostly chosen by the judges themselves.
Typically, they will take on the most difficult cases, with implications that stretch far beyond the parties involved in the dispute
As such, unanimous rulings are rare - although in the majority of cases the judges do not split along ideological lines.
Nevertheless, the court is seen to have liberal and conservative wings, which are currently evenly balanced with four judges each.
The appointment of Donald Trump's nominee Neil Gorsuch - if approved by the Senate - would tilt the balance back in favour of the conservatives.
That could be strengthened further if an opportunity arises for Mr Trump to make a second appointment during his tenure in the White House.
With the court expected to hear cases on voter rights, racial bias in policing and US immigration policy in the coming years, it could have a profound effect on the shape of future social policy.
Mr Trump’s campaign promise to select a conservative was widely seen to have been crucial in persuading evangelical Christians, who are concerned about issues such as the expansion of gay rights, to back him despite misgivings over his remarks about women.
They will now be looking to see if the court is prepared to revisit past rulings on issues such as abortion, as has been demanded by many anti-abortion activists.
However, the president may face a tough fight to get his man in place.
Democrats were infuriated when the Republicans refused even to vote on Barack Obama’s nominee for the vacant seat - the liberal judge Merrick Garland.
Senate minority leader Chuck Schumer has previously warned he would be willing to block confirmation and leave the seat open if Mr Trump does not name a "mainstream nominee".