Gene expression is regulated by genomic enhancers that recruit transcription factors and cofactors to activate transcription from target core promoters. Over the past years, thousands of enhancers and core promoters in animal genomes have been annotated, and we have learned much about the domain structure in which regulatory genomes are organized in animals. Enhancer–core-promoter targeting occurs at several levels, including regulatory domains, DNA accessibility, and sequence-encoded core-promoter specificities that are likely mediated by different regulatory proteins. We review here current knowledge about enhancer–core-promoter targeting, regulatory communication between enhancers and core promoters, and the protein factors involved. We conclude with an outlook on open questions that we find particularly interesting and that will likely lead to additional insights in the upcoming years.