We present results from a study of meson spectra and structure in the limit where one quark is infinitely heavy. The calculations, based on the framework of light-front QCD formulated on a transverse lattice, are the first non-perturbative studies of B mesons in light-front QCD. We calculate the Isgur-Wise form factor, light-cone distribution amplitude, the heavy-quark parton distribution function and the leptonic decay constant of B mesons.