In this paper, numerical modelling of left-handed materials (LHMs) is presented using in-house and commercial software packages. Approaches used include the finite-difference time-domain (FDTD) method, finite element method (FEM) and method of moments (MoMs). Numerical simulation includes verification of negative refraction and "perfect lenses" construction,investigation of evanescent wave behaviour in layered LHMs, reversed Snells Law in electromagnetic band gap (EBG)-like structures and construction of LHMs using modified split ring resonators (SRRs). Numerical results were verified to be in good agreement with theory. At the end of this paper, potential applications of LHMs in microwave engineering are discussed.