It is a well known fact that the solutions of Euler's equations admit discontinuities (shocks, contact discontinuities). Therefore it is not possible to use standard finite difference techniques to numerically advance solutions in time. One way to circumvent the problem is to introduce artificial viscosity that smoothes the discontinuities. Another possibility is to take advantage of the conservative formulation of the Euler's equations and use Godunov type finite volume methods. In this talk I will explain the latter approach and present several astrophysical applications. For certain type of calculations adaptive mesh refinment (AMR) is a necessity, and part of my talk will be devoted to the issue of incorporating AMR into the numerical scheme.