Temperatures in the range of 0.05 to 80 K are required for most applications of superconductors. Refrigeration powers range from fractions of a watt for many electronic applications to kilowatts for some large magnet and power applications. This paper reviews the various types of refrigeration methods currently available to meet the needs of various applications of superconductors. The methods covered include mainly the gas cycles, which are divided into the recuperative types (steady flow), such as the Joule- Thomson, Brayton, and Claude cycles, and the regenerative types (oscillating flow), such as Stirling, Gifford-McMahon, and pulse tube cycles. Methods for reaching millikelvin temperatures are briefly mentioned as well. The operating principles of the various methods are described, and the advantages and disadvantages of each are given to help the user understand which approach may work best for a particular application. All cryogenic refrigeration methods have a common set of problems that have hindered many applications of superconductors. These problems and recent developments to overcome some of these problems are discussed.