Over the past couple of decades, microfoundations have been all the rage in Economics, and in particular in Macroeconomics. The latter relied traditionally on reduced forms, which lead to the Lucas Critique: reduced form elasticities fail to account for elasticity changes that policy shifts can induce. It is now accepted in all fields of Economics that you need to build theory from the ground up, in particular by looking at preferences and constraints.
Of course, the next question is then where those preferences come from and under what circumstances they can change. Too often, the unexplained part in economic behavior is attributed to preference shocks, in part because we do not understand preference formation. Neuroeconomics is about understanding where preferences, and behaviors, come from, and possibly rewrite decision theory from the ground up.
As its name implies, this new field combines Economics and Neurology. It conducts economic experiments, where subjects need to take some decisions while their brain is scanned. Some researchers try to formulate the neurological phenomena during decision taking into formulas, and inferring decision theory from there, or invalidating it.
For general surveys on Neuroeconomics, see Colin Camerer in the Economic Journal, Camerer, Loewenstein and Prelec in the Journal of Economic Literature, and Douglas Bernheim. There are also dedicated research centers at Claremont, Stanford and George Mason. And even a Society for Neuroeconomics. The time of economists with lab coats has come.