Although there has been many advances in incorporating prior information into prioritization of trait-associated variants in genome wide association studies (GWAS), functional annotation data rarely played more than an indirect role in assessing evidence for association in these approaches. Furthermore, functional annotation has not been utilized at all in the joint analysis of GWAS and expression quantitative loci data, commonly known as genetical genomics data. This is a significant barrier in understanding the regulatory roles of variants. We consider two complementary models for systematically integrating functional annotation information into GWAS and mediation analysis of GWAS with eQTL. Our formulations focus on the challenging task of selecting among prior information that are most consistent with the data. This is critically important because large consortia projects are cataloging DNA elements of RNA transcription, DNA accessibility, chromatin states, and DNA methylation across wide variety of tissues at an unprecedented rate. We investigate the statistical properties of these models and quantify the statistical gain in terms of power and robustness.