A differential field is a field K with a derivation, that is, an additive map D:K→K satisfying D (fg )=D (f ) g +fD (g ) for f,g in K. The field of constants C of K is the kernel of D. A differential central simple algebra (DCSA) over K is a pair (A,D) where A is a central simple algebra and D is a derivation of A extending the derivation D of its center K. Any DCSA, and in particular a matrix differential algebra over K, can be trivialized by a Picard-Vessiot (differential Galois) extension E of K. In the matrix algebra case, there is a correspondence between K-algebras trivialized by E and representations of the differential Galois group of E over K in PGLn(C ), which can be interpreted as cocycles equivalent up to coboundaries. I will explain these results and discuss the `differential' Brauer group that can be associated to K. (This is joint work with Andy Magid).