This article provides a critical review of past and current techniques for the computational modeling of ligaments and tendons. A brief overview of relevant concepts from the fields of continuum mechanics and finite element analysis is provided. The structure and function of ligaments and tendons are reviewed in detail, with emphasis on the relationship of microstructural tissue features to the continuum mechanical behavior. Experimental techniques for the material characterization of biological soft tissues are discussed. Past and current efforts related to the constitutive modeling of ligaments and tendons are classified by the particular technique and dimensionality. Applications of one-dimensional and three-dimensional constitutive models in the representation of the mechanical behavior of joints are presented. Future research directions are identified.