This paper addresses technical problems of thermal contact conductance or resistance which inevitably occurs in most cryogenic engineering systems. The main focus of this paper is to examine what kind of physical factors primarily influences the thermal contact resistance and to suggest how it can be minimized. It is a good practical rule that the contact surface must have sub-micron roughness level with no oxide layer and be thinly covered by indium, gold, or Apiezon-N grease for securing sufficient direct contact area. The higher contact pressure, the lower the thermal contact resistance. The general description of this technique has been widely perceived and reasonable engineering results have been achieved in most applications. However, the detailed view of employing these techniques and their relative efficacies to reduce thermal contact resistances need to be thoroughly reviewed. We should consider specific thermal contact conditions, examine the engineering requirements, and execute each method with precautions to fulfil their maximum potentials.