An understandable starting point for this is the end of Modernism, that the historian Charles Jencks pronounced dead at 3.32pm on 15th March 1972. This is the time that the Modernist Pruitt-Igoe housing project in St.Louis, Missouri (US) was dynamited. Aside from critical theory written by academics, Postmodernism then began as an architectural movement.
The movements acceptance and use of contrasting styles, from classical to modern, is described by the architect Robert Venturi as 'both/and (rather than either/or)'. The latter arguably describes Modernist ideas, either they are Modernist or they are not. The V and A shows a great example of this Postmodern mix of styles with a recreation of Hans Hollein's façade from Strada Novissima, The Presence of the Past (1980) (below). This was part of the Biennale of Architecture in Venice.
Near to a projection of a clip from Ridley Scott's Postmodernist Blade Runner (1982) film are various displays that artists and designers made out of found materials and objects. My favourite of these is Ron Arad's Concrete Stereo (1983) (below), which links in well with the post-apocalyptic feel of the movie nearby.
I like Peter Shire's Bel Air chair (1981-2) designed for Memphis, the Italian design and architecture group. Whilst being typically kitsch for Postmodern design, it does however stay on the right side of 'tasteful' in my opinion.
Frank Schreiner's 'Consumer Rest Chair' (1990) (below), designed for Stiletto, sums up the increasing consumerism in western society in the late Twentieth Century...
...Indeed, the V and A states in its summary of the exhibition:
'as artists and designers embraced the wealth and status of the 1980's, Postmodernism collapsed under the weight of its own success'.