The design and implementation of biomedical devices for both diagnostic and direct medical applications have revolutionized patient care, paving the way for improved patient outcomes. Understanding the characteristics of materials used in the design of new devices is essential for their advancement. In this review, our goal is to assist biomedical researchers in appreciating the importance of these properties and the role of selecting the proper measurement. We discuss how the nanoscopic molecular composition, arrangement, and interactions generate the properties of liquids, solids, viscoelastic materials, and colloids and discuss the measurement techniques that can be used to assess these properties from the nanoscale to the macroscale. We explore the linear and nonlinear mechanical responses of materials, elucidate their behaviors under varying conditions, and discuss corresponding measurement techniques. Finally, we highlight the importance of tailoring measurements to the underlying biological processes and applications being investigated.