Maturity models and Information Technology (IT) service management models guide the definition and improvement of service management processes. Known approaches include ITIL, COBIT, ISO/IEC 20000, CMMI-SVC, and MR-MPS-SV. The implementation of these models results in benefits such as: increased user and customer satisfaction with IT services; financial savings due to less rework and less time used, and improved resource management and usage; improved decision making and optimized risk; and better alignment based on the business focus. However, some organizations find it difficult to use the models. This paper presents a study in which we identified critical factors for success and failure of the improvement of IT service processes. By doing a systematic mapping study and by snowballing, we were able to identify factors such as: project implementation strategy; support, commitment, and involvement; processes; and internal and external resources. Also, we analyzed our results using grounded theory procedures in order to facilitate their understanding.