Cis-regulatory elements (CRE), short DNA sequences through which transcription factors (TFs) exert regulatory control on gene expression, are postulated to be the major sites of causal sequence variation underlying the genetics of complex traits and diseases. We present integrative analyses, combining high-throughput genomic and epigenomic data with sequence-based computations, to identify the causal transcriptional components in a given tissue. We use data on adult human hearts to demonstrate that (1) sequence-based predictions detect numerous, active, tissue-specific CREs missed by experimental observations, (2) learned sequence features identify the cognate TFs, (3) CRE variants are specifically associated with cardiac gene expression, and (4) a significant fraction of the heritability of exemplar cardiac traits (QT interval, blood pressure, pulse rate) is attributable to these variants. This general systems approach can thus identify candidate causal variants and the components of gene regulatory networks (GRN) to enable understanding of the mechanisms of complex disorders on a tissue- or cell-type basis.