Full-waveform acoustic logging has made significant advances in both theory and application in recent years, and these advances have greatly increased the capability of log analysts to measure the physical properties of formations. Advances in theory provide the analytical tools required to understand the properties of measured seismic waves, and to relate those properties to such quantities as shear and compressional velocity and attenuation, and primary and fracture porosity and permeability of potential reservoir rocks. The theory demonstrates that all parts of recorded waveforms are related to various modes of propagation, even in the case of dipole and quadrupole source logging. However, the theory also indicates that these mode properties can be used to design velocity and attenuation picking schemes, and shows how source frequency spectra can be selected to optimize results in specific applications. Synthetic microseismogram computations are an effective tool in waveform interpretation theory; they demonstrate how shear arrival picks and mode attenuation can be used to compute shear velocity and intrinsic attenuation, and formation permeability for monopole, dipole and quadrupole sources. Array processing of multi-receiver data offers the opportunity to apply even more sophisticated analysis techniques. Synthetic microseismogram data is used to illustrate the application of the maximum-likelihood method, semblance cross-correlation, and Prony's method analysis techniques to determine seismic velocities and attenuations. The interpretation of acoustic waveform logs is illustrated by reviews of various practical applications, including synthetic seismogram generation, lithology determination, estimation of geomechanical properties in situ, permeability estimation, and design of hydraulic fracture operations.