Current thinking on beavers identifies them as a desirable resource as well as a species to be maintained. Beavers and their dam building provide benefits including storing water, restoring eroded streams, limiting erosion, extending wet cycles in streams, preserving meadows and wetlands and providing wildlife habitat.
We see beavers in a wide variety of places in California but it wasn't always so. Some questioned whether beaver were native above 1000 feet in the foothills and sierras and cascades. These conclusions were the result of near extirpation of beaver by trappers in the 19th century. The Hudson's Bay Company instructed their trappers to make a "fur desert" below the Columbia River so as to make the western states less attractive to the United States. They proved to be very successful and beaver were scarce by 1890. Trapping started about 1823 and continued through the 19th century. It wasn't all done by the Hudson Bay Company and many American trappers were active in California.
California Division of Fish and Game began studying beaver and attempting their placement throughout the state in about 1920. This placement resulted in the parachuting of 200 beaver into El Dorado County in 1950. We all can attest to the success of this program via their presence from the foothills to the mountains including in Southern California.
A comprehensive article on their history can be found here.