Abstract: I will discuss joint work in progress with Jakub Gismatullin and Patrick Simonetta on groups definable (in the home sort) in certain valued fields, such as ACVF and Q_p. Our main result is a description of simple definable groups which are linear, using Bruhat-Tits buildings and a result of Prasad. It appears to be open whether there is a nonlinear simple definable group.