Neutrino-driven winds are thought to accompany the Kelvin-Helmholtz cooling phase of nascent protoneutron stars in the first seconds after a core-collapse supernova . These outflows are a likely candidate as the astrophysical site for rapid neutron-capture nucleosynthesis ( the r -process ) . In this chapter we review the physics of protoneutron star winds and assess their potential as a site for the production of the heavy r -process nuclides . We show that spherical transonic protoneutron star winds do not produce robust r -process nucleosynthesis for ‘ canonical ’ neutron stars with gravitational masses of 1.4 M _ { \odot } and coordinate radii of 10 km . We further speculate on and review some aspects of neutrino-driven winds from protoneutron stars with strong magnetic fields .