The use of lattice approximations to study relativistic quantum field theories is surveyed. The models for scalar, gauge and fermionic degrees of freedom are defined. The standard methods for analytic study of these models using strong coupling, duality and mean field methods are outlined. The important area of numerical Monte Carlo simulations is also studied. These methods are used in the study of quantum chromodynamics in detail, including its spectrum. The arguments leading to the 'proof' that phi 4 is trivial theory are presented.