The superconducting transition temperatures Tc of some metals prepared in the form of small grains are appreciably higher than the ordinary values. The extremely small grain size gives rise to very short mean free paths and critical magnetic fields up to two orders of magnitudes larger than the thermodynamic critical fields. The critical fields and resistivities can be explained by a model which assumes tunneling between grains. Experiments indicate that the transmissivities of the tunneling barriers are large (≃10−1). Thus the grains are strongly coupled to each other, a finding which would appear to rule out enhancement of Tc due to quantization of electronic motion expected in small isolated systems. Other possible enhancement mechanisms discussed are: Josephson tunneling, surface enhancement of the electron-phonon interaction, and an increase in the electronic density of states due to atomic disorder. The relation between the somewhat unusual properties of granular superconductors and current application of thin films will be discussed.