These notes, based on a talk given at the Neutrino 2006 conference [Neutrino 2006, Santa Fe, New Mexico, USA, http://neutrinosantafe06.com/ ], review the sensitivity of solar neutrinos to certain types of new physics, namely modifications of neutrino-matter interactions by the exchange of a new heavy particle and a large neutrino transition moment. Both were first proposed in the 1970ʼs as possible explanations for the solar neutrino “problem” and were actively investigated for many years. While since ruled out as the dominant mechanisms of the solar neutrino flavor conversion, they remain of great interest as subdominant effects, which, if observed, would open a window to new physics. We outline the sensitivity of the current experiments and describe progress that may be expected in the near future.