We present a new semiempirical model for the dust continuum number counts of galaxies at 1.1 mm and 850 μm. Our approach couples an observationally motivated model for the stellar mass and star formation rate distribution of galaxies with empirical scaling relations to predict the dust continuum flux density of these galaxies. Without a need to tweak the IMF, the model reproduces the currently available observations of the 1.1 mm and 850 μm number counts, including the observed flattening in the 1.1 mm number counts below 0.3 mJy and the number counts in discrete bins of different galaxy properties. Predictions of our work include the following: (1) the galaxies that dominate the number counts at flux densities below 1 mJy (3 mJy) at 1.1 mm (850 μm) have redshifts between z = 1 and z = 2, stellar masses of ∼5 1010 M o˙, and dust masses of ∼108 M o˙; (2) the flattening in the observed 1.1 mm number counts corresponds to the knee of the 1.1 mm luminosity function. A similar flattening is predicted for the number counts at 850 μm; (3) the model reproduces the redshift distribution of current 1.1 mm detections; and (4) to efficiently detect large numbers of galaxies through their dust continuum, future surveys should scan large areas once reaching a 1.1 mm flux density of 0.1 mJy rather than integrating to fainter fluxes. Our modeling framework also suggests that the amount of information on galaxy physics that can be extracted from the 1.1 mm and 850 μm number counts is almost exhausted.