During this talk, we will discuss recent advancements in inverse problems for piezoelectric equations. Specifically, we will present a uniqueness result that pertains to recovering coefficients of piecewise homogeneous piezoelectric equations from a localized Dirichlet-to-Neumann map on partial boundaries. Additionally, we obtained a first-order perturbation formula for the phase velocity of Bleustein-Gulyaev (BG) waves in a specific hexagonal piezoelectric equation. This formula expresses the shift in velocity from its comparative value, caused by the perturbation of the elasticity tensor, piezoelectric tensor, and dielectric tensor. This work has been done in collaboration with G. Nakamura, K. Tanuma, and J. Xu.