A quantum‐statistical theory of microwave and millimeter‐wave detection using superconducting tunnel junctions is developed, with a rigorous account of quantum, thermal, and shot noise arising from fluctuation sources associated with the junctions, signal source, and matching circuits. The problem of the noise characterization in the quantum sensitivity range is considered and a general noise parameter &THgr;Nis introduced. This parameter is shown to be an adequate figure of merit for most receivers of interest while some devices can require a more complex characterization. Analytical expressions and/or numerically calculated plots for &THgr;Nare presented for the most promising detection modes including the parametric amplification, heterodyne mixing, and quadratic videodetection, using both the quasiparticle‐current and the Cooper‐pair‐current nonlinearities. Ultimate minimum values of &THgr;Nfor each detection mode are compared and found to be in agreement with limitations imposed by the quantum‐mechanical uncertainty principle.