Mechanical moduli of biological tissues and polymers are critically involved in various biological and engineering processes, such as disease progression, aging, tissue and cell engineering, drug delivery, as well as bonding and micro fabrication.  However, it has been difficult to measure the material properties that are heterogeneous in three-dimensional (3D) space and may vary over time, as this requires a noncontact noninvasive technique with high spatiotemporal resolution. Here we introduce biomechanical optical imaging based on Brillouin light scattering mediated by acoustic phonons inherently present in material.  Measuring the frequency shift and linewidth of Brillouin spectrum allows determining the viscoelastic properties of the material. In the past few years, we have developed a multistage parallel spectrometer with high spectral resolution (sub-GHz), 80-dB extinction and several-orders-of-magnitude higher throughput efficiency than conventional scanning interferometers.  The first area of biomedical applications we have investigated is ophthalmology where Brillouin microscopy enable measuring changes in corneal and lens elasticity by aging, by the progression of disease, or in response to treatment and drugs.  We are now transitioning to the characterization of intracellular and extracellular elasticity.