In the present talk we will give an introduction to numerical methods for hyperbolic conservation laws. In particular, we will concentrate on the so-called characteristics based finite volume methods for one- and two-dimensional problems. For the latter case, the theory of bicharacteristics is used in order to obtain a multidimensional time evolution of the solution. Applications to the Euler equations of gas dynamics, multi-layer shallow water equations used in oceanography or river flow modelling and acoustic equations will be presented. Numerical results illustrate high accuracy,stability and robustness of the proposed schemes. The experimental order of convergence confirm our theoretical results for error analysis for linearised problems.