The classical Local Langlands Correspondence for the group GL_2(Q_p) gives a bijection between certain complex representations of GL_2(Q_p) and certain two-dimensional complex representations of the absolute Galois group of Q_p. This correspondence satisfies many nice properties, and may be viewed as a "rank 2" analog of local class field theory. I'll briefly review these results, and then try to explain an equally interesting version of this correspondence with complex coefficients replaced by p-adic coefficients. Speaker(s): Karol Koziol (University of Michigan)