The all-sky monitoring capability of Fermi GBM makes it ideal for finding transients. Fermi GBM triggers on events such as gamma-ray bursts, soft gamma-ray repeaters, X-ray bursters, solar flares, and terrestrial gamma-ray flashes. A previous systematic search in offline data for X-ray bursts has uncovered untriggered gamma-ray bursts, and currently there is a dedicated offline search pipeline looking for weak transients undetected by the onboard trigger conditions. The untargeted search looks for significant signals in two or more detectors at various timescales in the continuous background-subtracted data. It detects $\sim80$ short GRB candidates per year in addition to the $\sim40$ short GRBs that trigger onboard. Since July 2017, these candidates are published by the GRB Coordinates Network as Fermi-GBM Subthreshold Notices, accompanied by localization maps and lightcurves. At present only short GRB candidates are published, expansion to long GRBs and other transient types are forthcoming.