GOFAI, or Good Old Fashioned AI, views the brain as a machine for processing symbols. The focus was on the programmer to analyse a problem, break it down into its component parts, and write code that would perform each of the component parts. It heavily relied upon Search techniques, which search through the possible solutions to a problem until a satisfactory answer is found.
As time went on, it became clear that GOFAI had severe limitations. If the Branching Factor of a problem is too large for GOFAI to search through, the only answer is to use Heuristics to search the solution space more efficiently. But if a suitable heuristic is not known, then there GOFAI gets stuck.
New Wave AI is still a relatively new field, and a lot of interesting work is still being done. Some of the more exciting developments include Chaotic Neural Networks, Gaseous Neural Networks and Situated Robotics.