Information is available via GOV.UK which explains the background to devolution and how the legislatures and administrations of Scotland, Wales and Northern Ireland work:
The Northern Ireland Assembly was established under the terms of the Belfast Agreement (also known as the Good Friday Agreement) and was first elected on 25 June 1998. Legislative powers and executive authority for the Northern Ireland Government Departments were devolved to the Assembly from 2 December 1999.
The second election to the Assembly was held on 26 November 2003, although the Assembly had been suspended since 14 October 2002 and it remained suspended after this election. The Northern Ireland (St Andrews Agreement) Act 2006 provided for a Transitional Assembly to take part in preparations for the restoration of devolved government, in accordance with the St Andrews Agreement.
This Transitional Assembly helped to create the conditions for a third Assembly election, which took place on 7 March 2007. Restoration took place on 8 May 2007. Further elections were held in 2011 and 2016. The resignation of the Deputy First Minister in January 2017 was followed by another election in March 2017; however, (as of December 2017) agreement on the formation of a new Executive has yet to be reached, and the new Assembly has not yet met.
After the May 1997 UK election, the Labour government arranged for a referendum on its proposals for Scottish devolution, which were set out in a White Paper in July 1997, Scotland's Parliament (Cm. 3658). The referendum, held on 11 September 1997, produced clear majorities for the two propositions: that a Scottish Parliament should be created, and that it should have certain tax-varying powers.
Following this result, the Scotland Bill was introduced to Parliament in December 1997 and became law as the Scotland Act in November 1998. The first elections for the Scottish Parliament were held on 6 May 1999, and the first meeting took place on 12 May. On 1 July, the Scottish Parliament was officially opened by Her Majesty The Queen and received its full legislative powers.
Image © Scottish Parliamentary Corporate Body – 2012. Licensed under the Scottish Parliament Copyright Licence
After the May 1997 UK election, a referendum was held on the Labour government's proposals for Welsh devolution, as set out in the White Paper A Voice for Wales (Cm. 3718). On 18 September 1997, a narrow majority voted in favour of a Welsh Assembly. Following this result, the Government of Wales Act 1998 was passed, leading to the first elections on 6 May 1999 and the first meeting of the National Assembly for Wales on 12 May. The official opening by Her Majesty the Queen took place on 26 May, and the powers of the Secretary of State for Wales were transferred to the Assembly on 1 July.
The Government of Wales Act 2006 gave the National Assembly powers to seek permission to create legislation on devolved issues in the form of Assembly Measures. It also established the Welsh Government, an executive body separate from the legislature, the National Assembly for Wales. On 3 March 2011 a further referendum was held and the people of Wales voted in favour of further law-making powers for the National Assembly, allowing it to make laws directly on all of the 20 areas (set out in the 2006 Act) for which the Welsh Government has responsibility.