The situation in solar neutrino science has changed drastically in the past decade, with results now available from five neutrino experiments that use different methods to look at different regions of the solar-neutrino energy-spectrum. While the goal of all of these experiments is physics, they all rely heavily on chemistry and radiochemistry. Three of these experiments are radiochemical, the 37Cl detector and the two different forms of 71Ga detectors used in GALLEX and SAGE are based on the chemical isolation and counting of the radioactive products of neutrino interactions. The other two, Kamiokande and its improved successor, Super- Kamiokande, detect neutrinos in real time; however, they also depend sensitively on radiochemistry in that (as in all the solar neutrino detectors) radioactive contaminants must be controlled at very low levels. It is noteworthy that all of these experiments (a) have detected solar neutrinos, but (b) all report deficits of the observed neutrinos relative to the predictions of standard solar models — the so-called "solar neutrino problem". In this paper, I review the basic principles of operation of these neutrino detectors, report their recent results, and discuss some of the interpretations that are now in vogue. I then describe some of the new neutrino detectors that are under construction or being developed, and discuss the kinds of new results we might expect to see in the early years of the new millennium.