Time-distance analysis is emerging as a powerful diagnostic tool in local helioseismology. By directly measuring propagation times of wave packets between selected locations at the surface of the sun, and their variations over specific areas, a directed diagnostic of the physical properties of the region below these areas can be achieved. We present and discuss inversion methodologies specific to time-distance analysis. These have been optimized for sparse matrices, and include error-bar computation as well as resolution kernel estimation. Our inversion methodology for velocity flow allow us to impose a mass-conservation constrain. We show the diagnostic potential of time-distance inversion and its limitation with various simulations. We illustrate the inversion resolving power potential and discuss the trade-off between resolution and error magnification, including the effect of imposing mass-conservation for velocity flow inferences. We also show inferences from actual observations obtained with the MDI experiment on board the SOHO spacecraft.