Dogs were domesticated at some point in prehistory; you might have better luck asking an archeologist or anthropologists than a historian for the current debate on this. Dogs have been seen as 'a member of the family' for a long time, just in a working sense as opposed to the purely pastoral image of pets we have today. In many cultures today they have to have some usefulness or else are just another mouth to feed. For instance in rural parts of Southeast Asia dogs are still primarily used for the purpose of guarding property; in Vietnam they are also a source of food (Source: own experience).

In Western Europe dogs were bred primarily to fulfil a certain function. Poodles were 'water retrievers' who's bushy hair helped them to stay afloat while hunting. The modern poodle began to take shape in the 15th and 16th centuries (as we can see in paintings by Durer) but it wasn't until they were imported to England in the 18th century that we get the 'miniature' and 'toy' versions which were less functional and more pet-like. The fashion for keeping dogs as pets grew in size among the upper classes during the 19th century, leading to the foundation of the Kennel Club in the UK in 1873, which defined the desired characteristics of individual breeds, and was followed by other Kennel Clubs in the US and elsewhere. Throughout the 20th century pet ownership was less confined to the affluent as people began to be able to afford pets as well as a shifting cultural view of animals, helped in part by the establishment of organisations such as the RSPCA or Humane Societies in the US. Harold Herzog claims that the media had a large role in this, citing the massive rise in Dalmation ownership after the release of 101 Dalmation in 1985. This led to the increase in dog ownership we have seen throughout the last century.

I hope this has gone at least some way to answering your question.

Source: Harold Herzog, Biology, Culture, and the Origins of Pet-Keeping