Context:The Unified Modeling Language (UML), with its 14 different diagram types, is the de-facto standard modeling language for object-oriented modeling and documentation. Since the various UML diagrams describe different aspects of one, and only one, software under development, they are not independent but strongly depend on each other in many ways. In other words, the UML diagrams describing a software product must be consistent. Inconsistencies between these diagrams may be a source of faults in software systems. It is therefore paramount that these inconsistencies be detected, analyzed and hopefully fixed. Objective: The aim of this article is to deliver a comprehensive summary of UML consistency rules as they are described in the literature to date to obtain an extensive and detailed overview of the current research in this area. Method: We performed a Systematic Mapping Study by following well-known guidelines. We selected 95 primary studies from a search with seven search engines performed in December 2012. Results: Different results are worth mentioning. First it appears that researchers tend to discuss very similar consistency rules, over and over again. Most rules are horizontal (98.10%) and syntactic (88.21%). The most used diagrams are the class diagram (71.58%), the sequence diagram (47.37%) and the state machine diagram (42.11%). Conclusion: The fact that many rules are duplicated in primary studies confirms the need for a well-accepted list of consistency rules. This paper is a first step in this direction. Results indicate that much more work is needed to develop consistency rules for all 14 UML diagrams, in all dimensions of consistency (e.g., semantic and syntactic on the one hand, horizontal, vertical and evolution on the other hand).