The human genome contains millions of candidate cis-regulatory elements (CREs) with cell-type-specific activities that shape both health and myriad disease states. However, we lack a functional understanding of the sequence features that control the activity and cell-type-specific features of these CREs. Here, we used lentivirus-based massively parallel reporter assays (lentiMPRAs) to test the regulatory activity of over 680,000 sequences, representing a nearly comprehensive set of all annotated CREs among three cell types (HepG2, K562, and WTC11), finding 41.7% to be functional. By testing sequences in both orientations, we find promoters to have significant strand orientation effects. We also observe that their 200 nucleotide cores function as non-cell-type-specific 'on switches' providing similar expression levels to their associated gene. In contrast, enhancers have weaker orientation effects, but increased tissue-specific characteristics. Utilizing our lentiMPRA data, we develop sequence-based models to predict CRE function with high accuracy and delineate regulatory motifs. Testing an additional lentiMPRA library encompassing 60,000 CREs in all three cell types, we further identified factors that determine cell-type specificity. Collectively, our work provides an exhaustive catalog of functional CREs in three widely used cell lines, and showcases how large-scale functional measurements can be used to dissect regulatory grammar.