Thermoelectric (Peltier) coolers have historically not been used for cooling to temperatures much below 200 K, because of limitations with existing thermoelectric materials. There are many advantages to solid-state coolers: they have no moving parts, are compact, vibration-free, inherently durable, and scalable to low power levels. A significant drawback is their low coefficient of performance. The figure of merit, zT, is the materials characteristic that sets this efficiency in Peltier coolers. The zT decreases rapidly with temperature, roughly following a T7/2 law. However, new material developments have taken place in the last decade that have made it possible to reach zT>0.5 down to 50 K. Many new ideas have also been put forward that enable better ZT’s and lower temperatures. This article reviews the difficulties associated with Peltier cooling at cryogenic temperatures, as an introduction to the following presentations and proceeding entries that will present solutions that have been developed since 2010.