Fast advances in polymer science have provided new hydrogels for applications in drug delivery. Among modern drug formulations, polymeric type stimuli-responsive hydrogels (SRHs), also called smart hydrogels, deserve special attention as they revealed to be a promising tool useful for a variety of pharmaceutical and biomedical applications. In fact, the basic feature of these systems is the ability to change their mechanical properties, swelling ability, hydrophilicity, or bioactive molecules permeability, which are influenced by various stimuli, particularly enzymes. Indeed, among a great number of SHRs, enzyme-responsive hydrogels (ERHs) gain much interest as they possess several potential biomedical applications (e.g., in controlled release, drug delivery, etc.). Such a new type of SHRs directly respond to many different enzymes even under mild conditions. Therefore, they show either reversible or irreversible enzyme-induced changes both in chemical and physical properties. This article reviews the state-of-the art in ERHs designed for controlled drug delivery systems (DDSs). Principal enzymes used for biomedical hydrogel preparation were presented and different ERHs were further characterized focusing mainly on glucose oxidase-, β-galactosidase- and metalloproteinases-based catalyzed reactions. Additionally, strategies employed to produce ERHs were described. The current state of knowledge and the discussion were made on successful applications and prospects for further development of effective methods used to obtain ERH as DDSs.