  Light-front formulations of quantum field theories have many advantages for
computing electroweak matrix elements of strongly interacting systems and other
quantities that are used to study hadronic structure. The theory can be
formulated in Hamiltonian form so non-perturbative calculations of the strongly
interacting initial and final states are in principle reduced to linear
algebra. These states are needed for calculating parton distribution functions
and other types of distribution amplitudes that are used to understand the
structure of hadrons. Light-front boosts are kinematic transformations so the
strongly interacting states can be computed in any frame. This is useful for
computing current matrix elements involving electroweak probes where the
initial and final hadronic states are in different frames related by the
momentum transferred by the probe. Finally in many calculations the vacuum is
trivial so the calculations can be formulated in Fock space.
  The advantages of light front-field theory would not be interesting if the
light-front formulation was not equivalent to the covariant or canonical
formulations of quantum field theory. Many of the distinguishing properties of
light-front quantum field theory are difficult to reconcile with canonical or
covariant formulations of quantum field theory.
  This paper discusses the resolution of some of the apparent inconsistencies
in canonical, covariant and light-front formulations of quantum field theory.
The puzzles that will be discussed are (1) the problem of inequivalent
representations (2) the problem of the trivial vacuum (3) the problem of
ill-posed initial value problems (4) the problem of rotational covariance (5)
the problem of zero modes and (6) the problem of spontaneously broken
symmetries.
