The thermodynamic temperature of the Sun's atmosphere rises from ~6000K at the visible surface to millions of degrees in its outer atmosphere, the corona. This hot coronal plasma then expands supersonically to become the solar wind; this wind acceleration process is ongoing to very high altitudes (~10 solar radii) There is no sufficient thermal energy source for this heating and expansion, however remote sensing measurements of the coronal magnetic field suggest that the magnetic energy density is more than enough. Most of the proposed coronal heating/acceleration models involve the kinetic dissipation of plasma waves or turbulence, a process that is poorly understood. I will discuss some of these mechanisms, the associated puzzles, and the state of the art in measurements. The physics of astrophysical coronae has broader application and may apply to coronae above accretion disks, and disk-black hole interfaces in collisionless accretion, for example. The coming decade will be a golden age for coronal and heliospheric physics. Several dedicated NASA space missions (STEREO, SDO, IRIS) and the NSF's Advanced Technology Solar Telescope will provide high spatial resolution magnetic field and plasma observations of the transition region and corona. The ESA Solar Orbiter and NASA Solar Probe Plus missions will dive deep into the heliosphere and make low altitude (to 9.5 solar radii) in situ measurements. I will describe the Solar Probe Plus mission and its measurements in some detail.