The analog of the nonrelativistic Hamiltonian H is the light-front operator P − − , which generates translations in light-front time. It is constructed from the Lagrangian for the chosen quantum field theory. The total light-front momentum of the system, P _ _ ≡ ≡ ( P + , P → → ⊥ ⊥ ) , is the sum of the single-particle light-front momenta. The total light-front energy P − − is fixed by the mass-shell condition to be ( M 2 + P ⊥ ⊥ 2 ) / P + , where M is the invariant mass of the system. The Schrödinger-like equation of light-front quantization is then P − − ψ ψ = M 2 + P ⊥ ⊥ 2 P + ψ ψ . This provides a foundation for a nonperturbative analysis of quantum field theories that is quite distinct from the lattice approach.