Events from the year 1737 in Scotland.

• Secretary of State for Scotland: vacant

• The Lord Provost of Edinburgh is debarred from office following the previous year's Porteous Riots.
• Aberdeen Royal Infirmary founded as Woolmanhill Hospital.
• Royal Society of Edinburgh formed as the Edinburgh Society for Improving Arts and Sciences and particularly Natural Knowledge.
• Kilmichael Bridge in Argyll built.^[1]
• Construction of a new Glasgow town hall begins.
• Andrew Rodger, a farmer on the estate of Cavers, south Roxburghshire, develops a winnowing machine for corn, called a 'fanner'.

• 25 March (bapt.) – William Forsyth, horticulturist (died 1804 in London)
• 17 July – John Bowes, 9th Earl of Strathmore and Kinghorne, born John Lyon (died 1776 at sea)
• 29 August – John Hunter, Royal Navy officer and governor of New South Wales (died 1821 in London)
• 14 September – Alexander Geddes, Catholic theologian and scholar (died 1802 in London)
• James Clark, physician and plantation owner in Dominica (died 1819 in London)
• John Donaldson, miniature painter (died 1801 in London)

• 29 January – George Hamilton, 1st Earl of Orkney, soldier (born 1666; died in London)
• 1 February – Hew Dalrymple, Lord North Berwick, judge and politician (born 1652)

• Allan Ramsay co-writes and edits the last volume of The Tea-Table Miscellany, a collection of Scots songs.

• Timeline of Scottish history