The merits of microcalorimetry below 1°K for high resolution spectroscopy has become widely recognized on theoretical grounds. By combining the high efficiency, broadband spectral sensitivity of traditional photoelectric detectors with the high resolution capabilities characteristic of dispersive spectrometers, the microcalorimeter could potentially revolutionize spectroscopic measurements of astrophysical and laboratory plasmas. In actuality, however, the performance of prototype instruments has fallen short of theoretical predictions and practical detectors are still unavailable for use as laboratory and space-based instruments. These issues are currently being addressed by the new collaborative initiative between LLNL, LBL, U.C.I., U.C.B., and U.C.D.. Microcalorimeters of various types are being developed and tested at temperatures of 1.4, 0.3, and 0.1°K. These include monolithic devices made from NTD Germanium and composite configurations using sapphire substrates with temperature sensors fabricated from NTD Germanium, evaporative films of Germanium-Gold alloy, or material with superconducting transition edges. A new approache to low noise pulse counting electronics has been developed that allows the ultimate speed of the device to be determined solely by the detector thermal response and geometry. Our laboratory studies of the thermal and resistive properties of these and other candidate materials should enable us to characterize the pulse shape and subsequently predict the ultimate performance. We are building a compact adiabatic demagnetization refrigerator for conveniently reaching 0.1°K in the laboratory and for use in future satellite-borne missions. A description of this instrument together with results from our most recent experiments will be presented.