Red blood cells (RBCs) deformability refers to the cells’ ability to adapt their shape to the dynamically changing flow conditions so as to minimize their resistance to flow. The high red cell deformability enables it to pass through small blood vessels and significantly determines erythrocyte survival. Under normal physiological states, the RBCs are attuned to allow for adequate blood flow. However, rigid erythrocytes can disrupt the perfusion of peripheral tissues and directly block microvessels. Therefore, RBC deformability has been recognized as a sensitive indicator of RBC functionality. The loss of deformability, which a change in the cell shape can cause, modification of cell membrane or a shift in cytosol composition, can occur due to various pathological conditions or as a part of normal RBC aging (in vitro or in vivo). However, despite extensive research, we still do not fully understand the processes leading to increased cell rigidity under cold storage conditions in a blood bank (in vitro aging), In the present review, we discuss publications that examined the effect of RBCs’ cold storage on their deformability and the biological mechanisms governing this change. We first discuss the change in the deformability of cells during their cold storage. After that, we consider storage-related alterations in RBCs features, which can lead to impaired cell deformation. Finally, we attempt to trace a causal relationship between the observed phenomena and offer recommendations for improving the functionality of stored cells.