  We examine the current state-of-the-art in nonperturbative calculations done
with Hamiltonians constructed in light-front quantization of various field
theories. The language of light-front quantization is introduced, and important
(numerical) techniques, such as Pauli--Villars regularization, discrete
light-cone quantization, basis light-front quantization, the light-front
coupled-cluster method, the renormalization group procedure for effective
particles, sector-dependent renormalization, and the Lanczos diagonalization
method, are surveyed. Specific applications are discussed for quenched scalar
Yukawa theory, $\phi^4$ theory, ordinary Yukawa theory, supersymmetric
Yang--Mills theory, quantum electrodynamics, and quantum chromodynamics. The
content should serve as an introduction to these methods for anyone interested
in doing such calculations and as a rallying point for those who wish to solve
quantum chromodynamics in terms of wave functions rather than random samplings
of Euclidean field configurations.
