Viscosity and elasticity of biological tissues will change during onset and progression of many diseases. Viscoelasticity measurement of biological tissues plays an important role in diagnosis of diseases. We particularly review some basic principles and recent advances of viscoelasticity measurement based on laser speckle techniques from three aspects: difference of laser speckle contrast under elastic waves, optical intensity autocorrelation curve under Brownian motion, and laser speckle shift under low frequency oscillation stress.