We show that nonuniform Alfv¿n speed gradients across field lines generally arise from the evolution of Alfv¿n waves. The evolution of a group of nonlinear Alfv¿n waves with the same sign of parallel wavenumber generate small-amplitude pressure-balanced structures (PBSs) which cause the speed variations. This always causes refraction. In most cases, the Alfv¿n waves also couple to magnetosonic waves and acquire a weak compressional component and can undergo resonant absorption or transfer, wherein wave energy can propagate across field lines. At large amplitudes the waves also generate imbedded rotational discontinuities (RDs). Some of these RDs can be dissipated owing to resonant transfer. This process could partly contribute to the observed decrease of solar wind RDs with increasing distance from the Sun. Resonant transfer also triggers a cascade due to steepening, which leads to sustained proton heating. The cascade produces oblique and large wavenumber waves which travel in different directions and have associated compressions. Protons interact with these by pitch angle scattering. They gain energy from second-order Fermi acceleration and from Landau and transit time damping. Oblique waves are inferred to be present in the dissipation range of Alfv¿nic fluctuations at 1 AU. We argue that the process of proton heating should proceed similarly to simulation results. We also propose a role for the wave imbedded RD in coronal heating through its formation in the chromosphere and its likely dissolution in the corona where wave amplitudes are very small. ¿ 2001 American Geophysical Union