It has been known for over 50 years that the outer atmosphere of the Sun, the so-called corona, has a temperature of 106K (~0.1 keV) yet the exact reasons for this are still being debated. The magnetic field that pervades the corona is certainly the source of the heating, but the question is whether the field energy is dissipated via numerous, small, random reconnections (known as `nanoflares', i.e. small energy releases of about 1016J) or the damping of magnetohydrodynamic (MHD) waves propagating up from the Sun's surface layers (the photosphere). Some new evidence from the SOHO and Yohkoh spacecraft, with instruments on board which image the Sun in the extreme ultraviolet and soft x-rays, are shedding new light on the problem - it appears that the energy spectrum of small flare-like phenomena may be such that nanoflares are sufficiently numerous to supply the corona's energy requirements. However, these new findings do not preclude the possibility of MHD wave motions also supplying significant amounts of energy. Theory suggests very short period (<1 s) MHD waves are implicated in the heating process if so. Searches during total solar eclipses for modulations of the white-light coronal intensity that may result are being made with increasingly sophisticated equipment. Some very fast imaging systems are now available, and a description is given of a charge-coupled device camera experiment conducted successfully during the recent total solar eclipse visible in Europe.