  We prove the existence of a global bifurcation branch of $2\pi$-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 H\"older class $C^{\alpha}$, $\alpha <
\frac{1}{2}$. 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.
