The Arts and Crafts movement began in England during the second half of the nineteenth century. It was a reaction to industrialization and mass-production, and as such it emphasized hand made items and craftsmanship. The most famous name of this first phase of the Arts and Crafts era is William Morris. Another well-known name is Charles Rennie Mackintosh.

As the Arts and Crafts influence spread to America, much of the style was simplified until it became what is often known as the Craftsman style, after Gustav Stickley's Craftsman magazine. "Mission" is another name for this style, though "Mission" is often confused with Southwest style, so "Craftsman" may be a clearer term to use.

Frank Lloyd Wright's early works were certainly in the realm of Arts & Crafts style, and his later work can easily be seen as a continuation of A&C ideas.

In about 1900-1920, the Craftsman style was very popular in the US, especially in Western cities like Seattle, Portland, and Los Angeles that were being built up at that time. The stereotypical Craftsman house, the bungalow, is commonplace in the old neighborhoods of these cities.

The Craftsman/Mission/Arts and Crafts style has had a strong comeback in the 1990s. Many people are buying old bungalows and restoring them, filling them with Stickley furniture or modern reproductions thereof.

The Arts and Crafts movement overlapped quite a bit with the Art Nouveau movement and the Pre-Raphaelites, so you may want to check those categories for information about this era.