For native and engineered biological tissues, there exist many physiological, surgical, and medical device applications where multiaxial material characterization and modeling is required. Because biological tissues and many biocompatible elastomers are incompressible, planar biaxial testing allows for a two-dimensional (2-D) stress-state that can be used to fully characterize their three-dimensional (3-D) mechanical properties. Biological tissues exhibit complex mechanical behaviors not easily accounted for in classic elastomeric constitutive models. Accounting for these behaviors by careful experimental evaluation and formulation of constitutive models continues to be a challenging area in biomechanical modeling and simulation. The focus of this review is to describe the application of multiaxial testing techniques to soft tissues and their relation to modern biomechanical constitutive theories.