We are developing superconducting direct detectors for submillimeter astronomy that can in principle detect individual photons. These devices, Single Quasiparticle Photon Counter (SQPC), operate by measuring the quasiparticles generated when single Cooper-pairs are broken by absorption of a submillimeter photon. This photoconductive type of device could yield high quantum efficiency, large responsivity, microsecond response times, and sensitivities in the range of 10-20 Watts per root Hertz. The use of antenna coupling to a small absorber also suggests the potential for novel instrument designs and scalability to imaging or spectroscopic arrays. We will describe the device concept, recent results on fabrication and electrical characterization of these detectors, issues related to saturation and optimization of the device parameters. Finally, we have developed practical readout amplifiers for these high-impedance cryogenic detectors based on the Radio-Frequency Single-Electron Transistor (RF-SET). We will describe results of a demonstration of a transimpedance amplifier based on closed-loop operation of an RF-SET, and a demonstration of a wavelength-division multiplexing scheme for the RF-SET. These developments will be a key ingredient in scaling to large arrays of high-sensitivity detectors.