Hyperhydricity is the most common physiological disorder in in vitro plant cultivation. It is characterized by certain anatomical, morphological, physiological, and metabolic disturbances. Hyperhydricity significantly complicates the use of cell and tissue culture in research, reduces the efficiency of clonal micropropagation and the quality of seedlings, prevents the adaptation of plants in vivo, and can lead to significant losses of plant material. This review considers the main symptoms and causes of hyperhydricity, such as oxidative stress, impaired nitrogen metabolism, and the imbalance of endogenous hormones. The main factors influencing the level of hyperhydricity of plants in vitro are the mineral and hormonal composition of a medium and cultivation conditions, in particular the aeration of cultivation vessels. Based on these factors, various approaches are proposed to eliminate hyperhydricity, such as varying the mineral and hormonal composition of the medium, the use of exogenous additives, aeration systems, and specific lighting. However, not all methods used are universal in eliminating the symptoms of hyperhydricity. Therefore, the study of hyperhydricity requires a comprehensive approach, and measures aimed at its elimination should be complex and species-specific.