Over the past few decades, microrheology has emerged as a widely used technique to measure the mechanical properties of soft viscoelastic materials. Optical tweezers offer a powerful platform for performing microrheology measurements and can measure rheological properties at the level of single molecules out to near macroscopic scales. Unlike passive microrheology methods, which use diffusing microspheres to extract rheological properties, optical tweezers can probe the nonlinear viscoelastic response, and measure the space- and time-dependent rheological properties of heterogeneous, nonequilibrium materials. In this Viewpoint, I describe the basic principles underlying optical tweezers microrheology, the instrumentation and material requirements, and key applications to widely studied soft biological materials. I also describe several sophisticated approaches that include coupling optical tweezers to fluorescence microscopy and microfluidics. The described techniques can robustly characterize noncontinuum mechanics, nonlinear mechanical responses, strain-field heterogeneities, stress propagation, force relaxation dynamics, and time-dependent mechanics of active materials.