The adjoint-state method was introduced in the theory of inverse problems to efficiently compute the gradient of a functional without constructing Fréchet derivatives. This method now has been combined with numerical techniques to solve large-scale non-linear optimization problems based on physical equations. In this talk, I will first briefly introduce the use of the adjoint-state method in Eikonal equation based traveltime tomography and wave equation based adjoint tomography. Then, I will present two applications of the adjoint-state method to seismic anisotropic tomography in volcanic regions, including (1) P-wave azimuthal anisotropy in the Sierra Nevada and Walker Lane (Long Valley Caldera) based on adjoint-state traveltime tomography and (2) Shear-wave radial anisotropy beneath the Toba Caldera from ambient noise adjoint tomography.