Fresh cellular food materials including fruits and vegetables and animal tissues normally consist of fine organized cellular structures. Freezing is a common method to preserve the quality and safety of these cellular foods. However, the formation of ice crystals during food freezing may cause damage to the food microstructure, leading to the deterioration of food quality after thawing. This review offers current knowledge on freezing damage to cell structure of fresh cellular food materials. Effects of cell structure and water distribution on the texture and sensory properties of fresh cellular foods are presented. Mechanisms of cell structure damages caused by freezing are discussed. Novel methods to control the formation of ice crystals and preserve cell structures are also provided. The quality of cellular foods after frozen-thawed is highly correlated with the integrity and viability of tissue cells. The formation of ice crystals, water migration and the inherent characteristics of cell structure are regarded as the main factors affecting the cell structure during freezing. For obtaining better quality of frozen products, further investigation and understanding on freezing damage to cell structure of fresh cellular foods is necessary. It is hoped that the current review will provide more information on improving frozen food quality for the frozen food industry. •Cell damage during freezing causes quality deterioration of cellular foods.•Effects of cell structure and water distribution on food quality are presented.•Mechanisms of cell damage caused by freezing are discussed.•Novel methods to minimize the freezing damage to cell structure are assessed.•Further research are needed for improving the quality of frozen products.