Bioengineered materials represent an innovative option to support the regenerative processes of damaged tissues, with the final objective of creating a functional environment closely mimicking the native tissue. Among the different available biomaterials, hydrogels represent the solution of choice for tissue regeneration, thanks to the easy synthesis process and the highly tunable physical and mechanical properties. Moreover, hydrogels are biocompatible and biodegradable, able to integrate in biological environments and to support cellular interactions in order to restore damaged tissues’ functionality. This review offers an overview of the current knowledge concerning hydrogel synthesis and characterization and of the recent achievements in their experimental use in supporting skin, bone, cartilage, and muscle regeneration. The currently available in vitro and in vivo results are of great interest, highlighting the need for carefully designed and controlled preclinical studies and clinical trials to support the transition of these innovative biomaterials from the bench to the bedside.