In this chapter, we study partially ordered commutative residuated integral monoids known as pocrims. Pocrims are utilized in the study of ordered algebraic structures and have applications in various fields, including algebraic logic and reasoning, representation theory, and category theory, particularly in studying enriched categories, and computer science. For instance, hoops, BL-algebras, and MV-algebras are specific subclasses of pocrims, and they play a significant role in fuzzy logic and other areas of non-classical logic. On the other hand, pocrims have a close connection with BCK-algebras, which will be studied in the last section of this chapter. It is important to note that while pocrims offer a powerful tool for modeling uncertainty and imprecision, their applications are still an active area of research.