Since its inception more than a century and a half ago, photography has increasingly filled our lives. Today, we take photographs on mobile phones, displaying the results on computer screens. Yet the reasons why we take photographs have remained much the same: to commemorate, celebrate and preserve, for scientific functions, and to create art. In the process, this important exhibition suggests, we have also created a "family album" of changing Britishness.

The curators' selection of more than 500 images mostly opts for detail rather than the epic sweep (except Captain Alfred George Buckham's astonishingly cinematic 1925, Aerial View of Edinburgh and Dan Holdsworth's digitized aerial of London, A Machine for Living, untitled, 1999), for the domestic rather than the corporate or directly political.

From William Henry Fox Talbot's Construction of Nelson's Column, 1845, such pioneers as Julia Margaret Cameron, Lewis Carroll and Francis Frith, or more modern virtuosi as David Bailey and Norman Parkinson, mingle with lesser-known documenters of landscapes and city scenes, high society and low life.

Victorian society portraits reflect wealth and status in exotic drawing-room costume dramas and fancy-dress parties, but portraiture was adapted for grimmer purposes in early 20thcentury scientific and social records: images of asylum inmates taken for the Criminal Records Office (1912) show women in long skirts whose expressions reveal their troubled states of mind, while pocket-sized snaps of leading Suffragettes helped the police identify "trouble-makers".

The explosion of colour film and processing transformed photography. Colour transformed fashion shots, and helped launch the chocolate box clichés of the country garden idyll, but many photographers clung to black and white film for documentary or reportage.

Reportage is a key element in this exhibition, with the 1930s yielding some rich work, such as Wolfgang Suschitzky's bowlerhatted Man outside Foyle's and Edith Tudor-Hart's poor London family in a one-room flat.

High-street portrait studios of the 1950s reflected other social changes: Britain's new immigrants who wanted photos to send home. Eileen Power's Red black and green (1957) shows an awkward father with two dressed-up kids, while Tony Walker portrays a young Bradford nurse in uniform: signs both of anxiety and success. Horace Ové's later colourful documentary of the new community's street life is determinedly optimistic - Walking Proud.

This splendid show leaves us in the land of YouTube and instant photography. The scale has expanded from the 1840s post-cards to Alastair Thain's huge, digital portraits of three adolescents, Marine (2005), a timeless reminder, though, that working-class young men still go to war.

• Until 2 September. www.tate.org