The formation of DNA loops by proteins bound at distant sites along a single molecule is an essential mechanistic aspect of many biological processes including gene regulation, DNA replication, and recombination. The biological importance of DNA loop formation is underscored by an abundance of architectural proteins in cells such as HU, IHF, and HMGs, which facilitate looping by bending the intervening DNA between cognate protein-binding sites. We have developed a rigorous theory for DNA loop formation that connects the global mechanical and geometric properties of both DNA and protein, including previously neglected phenomena such as conformational flexibility of protein domains. Applications to problems in gene regulation and DNA recombination both in vitro and in vivo will be discussed.