Aggregation of information represented by membership functions is a central matter in intelligent systems where fuzzy rule base and reasoning mechanism are applied. Typical examples of such systems consist of, but not limited to, fuzzy control, decision support and expert systems. In most cases, the aggregation operators are defined on a pure axiomatic basis and are interpreted either as logical connectives (such as t-norms and t-conorms) or as averaging operators allowing a compensation effect (such as the arithmetic mean). On the other hand, it can be observed by some empirical tests that the above-mentioned classes of operators differ from those ones that people use in practice. Therefore, it is important to find operators that are, in a sense, mixtures of the previous ones, and allow some degree of compensation. This chapter summarizes fundamental as well as non-conventional classes of aggregation functions for fuzzy information. This includes, but is not limited to, the class of uninorms and nullnorms, absorbing norms, distance- and entropy-based operators, quasi-conjunctions and nonstrict means.