Herein We Review Some Recent Progress In Delineating Quantitatively The Effects Of Crystallographic Texture On The Acoustoelastic Coefficients Of Polycrystals. A General Constitutive Equation In Acoustoelasticity Has Been Derived For Weakly-Textured Orthorhombic Aggregates Of Cubic Crystallites. Besides The Initial Stress, This Constitutive Equation Contains Seven Texture Coefficients And Twelve Material Constants. Two Micromechanical Models Are Currently Available To Estimate These Material Constants From The Second-Order And Third-Order Elastic Constants Of The Constituting Crystallites. The Predicted Values Of Two Rayleigh-Wave Acoustoelastic Coefficients Are InGood Agreement With The Results Of Measurements On Two Samples Of 6061-T6 Aluminum Alloy.