Although cocoa butter (CB) has remarkable physical properties, its high price, growing difficulties, and increased consumption have been the main incentive to explore alternatives to replace or improve it. The potential of fats systems obtained from tropical butters, mixtures of them with vegetable oils, or marine fats as cocoa butter equivalent (CBE), extender (CBEx), substitute (CBS), replacer (CBR), or improver (CBI) have been deeply investigated and their physical chemical properties have been compared to those of CB. The TAGs composition of fats systems is a key factor that determines fats crystallization and polymorphic behaviors, and the suitability for an application. Fats with high concentrations of the TAGs StOSt, StOA, or StOB and low concentrations of POP compared to CB show some incompatibility with CB as analyzed by iso‐solid diagrams and a more complex polymorphic behavior. The presence of low melting TAGs such as POO, StOO, and AOO also leads to significant differences in physical behavior compared to CB. In those fats systems, co‐crystallization and polymorphic transitions of co‐existing solid solutions were reported. A few of the studied fat systems may behave as CBE. However, most of them have potential as CBS, CBR, CBEx or CBI in confectionery products. Studies reported the relevance of fractionation and interesterification processes to modify TAGs composition and the need of finding the right processing conditions and additives to extend fats applications.