Nicola Sturgeon declared the SNP has "made history" by winning a third term in government at Holyrood but the party failed to reach a majority.
The Scottish Conservatives had their best ever result, securing 31 MSPs, while Labour suffered its worst result since devolution with 24 MSPs.
Prime Minister David Cameron has congratulated Scottish Tory leader Ruth Davidson an securing an "historic result" for the party.
The Conservatives more than doubled their number of seats in the Scottish Parliament elections, up to 31 from the 15 secured in 2011.
It puts the Tories in second place at Holyrood for the first time since devolution.
21-year-old Ross Greer has been elected as the youngest-ever Member of the Scottish Parliament (MSP), representing the Green Party.
Labour is facing a disastrous election night in Scotland, with the party in danger of finishing third behind the SNP and the Conservatives.