  Parker's initial insights from 1958 provided a key causal link between the
heating of the solar corona and the acceleration of the solar wind. However, we
still do not know what fraction of the solar wind's mass, momentum, and energy
flux is driven by Parker-type gas pressure gradients, and what fraction is
driven by, e.g., wave-particle interactions or turbulence. SOHO has been
pivotal in bringing these ideas back to the forefront of coronal and solar wind
research. This paper reviews our current understanding of coronal heating in
the context of the acceleration of the fast and slow solar wind. For the fast
solar wind, a recent model of Alfven wave generation, propagation, and non-WKB
reflection is presented and compared with UVCS, SUMER, radio, and in-situ
observations at the last solar minimum. The derived fractions of energy and
momentum addition from thermal and nonthermal processes are found to be
consistent with various sets of observational data. For the more chaotic slow
solar wind, the relative roles of steady streamer-edge flows (as emphasized by
UVCS abundance analysis) versus bright blob structures (seen by LASCO) need to
be understood before the relation between streamer heating and and slow-wind
acceleration can be known with certainty. Finally, this presentation summarizes
the need for next-generation remote-sensing observations that can supply the
tight constraints needed to unambiguously characterize the dominant physics.
