We prove the existence of a global bifurcation branch of 2π-periodic,
smooth, traveling-wave solutions of the Whitham equation. It is shown that any subset of
solutions in the global branch contains a sequence which converges uniformly to some
solution of Hölder class Cα, α < 1/2. Bifurcation formulas are given, as well as some properties along the
global bifurcation branch. In addition, a spectral scheme for computing approximations to
those waves is put forward, and several numerical results along the global bifurcation
branch are presented, including the presence of a turning point and a ‘highest’, cusped
wave. Both analytic and numerical results are compared to traveling-wave solutions of the
KdV equation.