Cryopreservation plays an important role in tissue banking and will assume even greater importance when tissue engineering becomes an everyday reality. For some tissue grafts, living cells are unnecessary and adequate preservation methods are usually available. For other tissues living and functioning cells are needed and preservation methods are much less advanced. The basic requirements for cell recovery can usually be defined if a few basic biophysical properties of the cell are known and some standard measurements of the effect of cryobiological variables are carried out. The problems in tissue cryopreservation are not usually due to difficulties in preserving the living cells per se, but arise from the properties of the integrated cell/matrix systems upon which tissue function almost always depends. Some examples of such difficulties are described. It is concluded that the formation of ice, through both direct and indirect effects, is probably fundamental to these difficulties, and this is why vitrification seems to be the most likely way forward. However, two major problems still to be overcome are cryoprotectant toxicity and recrystallization during rewarming. Less obvious, and certainly less well understood is chilling injury - damage caused by reduction in temperature per se; this may yet turn out to be of fundamental importance.