Software measurement processes are crucial to plan, organize, monitor, control and improve software processes, products and resources. However, the successful implementation of software measurement processes is a challenging task in small and medium enterprises (SMEs). This paper presents a systematic mapping study to identify the significant factors and challenges of successful implementation of measurement processes. In total, 24 primary studies are analyzed after applying the mapping process. The most important success factors are measurement planning, measurement maturity, and budget allocation to implement a measurement process. This study aims to help SMEs to conduct a feasibility study before planning a measurement process.