A discretization of continuous-time models is an important issue for numerical simulations of dynamical systems as well as for digital implementation of control laws. Continuous-time homogeneous systemsHomogeneous system have specific features such as finite/fixed-time convergence, which may be destroyed by improper discretizationDiscretization. This chapter studies the problem of the so-called consistent discretizationConsistent discretization of asymptotically stable homogeneous systemsHomogeneous system, which preserve the convergence rate of the continuous-time system in its discrete-time counterpart. The classical Euler methods are shown to be inconsistent in the above sense. However, their combinations with a special coordinate transformation provide the desired discretizationDiscretization algorithms.