The exterior of church is notable for its magnificent neoclassical portico, complete with a colonnade of Corinthian columns in the style of an ancient Graecian temple.

The congregation has been actively involved in social justice issues, such as the Make Poverty History campaign in 2005 and events surrounding the 2021 United Nations Climate Change Conference.

Wellington operates the Crypt Café catering mostly to the local student and academic population at Glasgow University during weekdays from breakfast to lunch.

[3] Since 2004, Wellington has hosted the International Welcome Club, an initiative to "extend the hand of Christian friendship to anyone new to the city - student, migrant worker, asylum seeker or visitor from anywhere" by offering informal free English language tuition online via Zoom on Wednesdays, face to face in the Crypt Café on Thursdays, and via other seasonal events.

The prior minister was the Reverend Leith Fisher, who retired in October 2006 and died on 13 March 2009, following a road collision on the Isle of Arran.

His memorial service held at Wellington was attended by over 1,000 people and was conducted by the Right Reverend David Lunan, Moderator of the General Assembly of the Church of Scotland.