A central goal in human genetics is the identification of variants and genes that influence the risk of polygenic diseases. In the past decade, genome-wide association studies (GWAS) have identified tens of thousands of genetic loci associated with various diseases. Since the majority of such loci lie within non-coding regions and have many candidate variants in linkage disequilibrium, it has been challenging to accurately identify specific causal variants and genes. To aid in their discovery a variety of statistical and experimental approaches have been developed. These approaches often borrow information from functional genomics assays such as ATAC-seq, ChIP-seq and RNA-seq to annotate functional variants and identify regulatory relationships between variants and genes. While such approaches are powerful, given the diversity of cell types and environments, it is paramount to select disease-relevant contexts for follow-up analyses. In this review, we discuss the latest developments, challenges, and best practices for determining the causal mechanisms of polygenic disease risk variants with functional genomics data from specialized cell types.