Software systems are often modeled as a set of related UML diagrams. Due to the overlapping multi-view nature of UML and due to the incremental and iterative nature of the used software development process, these diagrams might contain inconsistencies. Thus, it is of utmost importance to detect, analyze and fix these inconsistencies before implementing the system. In this paper, we elaborate a transverse view of the aforementioned activities. More explicitly, this work proposes a Systematic Literature Review (SLR) that evaluates the existing techniques for managing inconsistencies using different research questions. The ultimate objective of this review is to come up with new recommendations that should be taken into consideration when conceiving a new proposal for checking inconsistencies.