Circa 1887, Victorian England - Mycroft Holmes defining trait is not his brilliance (which overshadows Sherlock's) but his laziness. Conan-Doyle has suitably placed him as an government official (auditing dept.) at Whitehall, and unsurprisingly - he is fat (Heavily built and massive, there was a suggestion of uncouth physical inertia in the figure). Mycroft resides at Pall Mall - less than a kilometer from his workplace (according to Google Maps) and is a founding member of the Diogenes Club situated across his residence.
The club as described by Sherlock Holmes in The Adventure of the Greek Interpreter: There are many men in London, you know, who, some from shyness, some from misanthropy , have no wish for the company of their fellows. Yet they are not averse to comfortable chairs and the latest periodicals. It is for the convenience of these that the Diogenes Club was started, and it now contains the most unsociable and unclubbable men in town. No member is permitted to take the least notice of any other one. Save in the Stranger's Room, no talking is, under any circumstances, allowed, and three offences, if brought to the notice of the committee, render the talker liable to expulsion. My brother was one of the founders, and I have myself found it a very soothing atmosphere.
Mycroft first appeared in The Adventure of the Greek Interpreter, where Sherlock and Watson meet him at the Diogenes Club and its quickly made known to the reader that despite his unimpressive exterior and boring profession - the government cannot function without him. Mycroft's specialty is the connections he can make between seemingly unconnected topics and advise the government on possible outcomes of actions in situations involving multiple variables, countries, technologies etc. This of course, is only made possible because of his ability to absorb, store and index information.
Mycroft appeared in four out of sixty Sherlock Holmes stories but made a disproportionately larger impact. Mycroft Holmes appears in many Sherlock Holmes films, where he has been played by acclaimed actors like Robert Morley, Charles Gray and Stephen Fry. Mycroft also has his own novels, written by authors like Kareem Abdul-Jabbar / Anna Waterhouse, Quinn Fawcett (Chelsea Quinn Yarbro & Bill Fawcett), Ray Walsh and Michael P. Hodel. He also has a role in Alan Moore's The League of Extraordinary Gentlemen.