The best overview of the topic I know of is https://www.microsoft.com/en-us/research/wp-content/uploads/..., which describes the state of the field ~18 months ago.

The major field where it's already being applied is in automating the conversion of data--building the program that can take "John Doe" and turn it into "<name>John</name> <surname>Doe</surname>" just by example. You can also do similar generalization to automate things like constructing highly repetitive graphics (e.g., draw a few teeth of a gear and the program does the rest). Superoptimization is the other main prong, where you really combine the synthesis and the verification to get correct faster code.