The extracellular matrix (ECM) and its mechanical properties play an important role in regulating the cellular responses that occur during tissue regeneration, wound healing, and disease progression. A growing body of research, especially in the fields of mechanobiology and matrix biology, has been devoted to elucidating how the ECM mechanical environment, both in vitro and in vivo, influences cell fate and function. Synthetic materials that faithfully recapitulate key mechanical properties of native tissues provide an important means to understand the mechanisms by which cells sense and remodel their surrounding mechanical environments. However, tissue mechanics is inherently complex, exhibiting dependencies on many timescales. This review highlights recent progress in synthetic biomaterials, particularly polymer networks that capture critical aspects of the dynamic mechanical properties of soft tissues by exploiting dynamic covalent chemistries. Finally, future directions and opportunities in the development and application of viscoelastic biomaterials are discussed.