Context: Multiple types of processing units (e.g., CPUs, GPUs and FPGAs) can be used jointly to achieve better performance in computational systems. However, these units are built with fundamentally different characteristics and demand attention especially towards software deployment. Objective: The goal of this work is to summarize the state-of-the-art of software deployment on heterogeneous platforms. We provide an overview of the research area by searching for and categorizing relevant studies, as well as discussing gaps and trends of the field. We are interested in the main concerns (RQ1) and the approaches used (RQ2) when deploying software on heterogeneous platforms. Method: In order to achieve our goal, we performed a systematic mapping study, which refers to a method for reviewing literature with basis on predefined search strategies and a multi-step selection process. Results: We selected and analyzed 146 primary studies from multiple sources and found that the area of research is dominated by solution proposals. The majority of the studies discuss concerns about scheduling, the quality of the software, and its architecture. A large number of studies focuses on the problem of scheduling tasks and processes. We found approaches that are applied at different binding times (i.e., design time, runtime, orthogonal). Conclusion: The evaluation of the proposed solutions in an industrial context is missing. Also, the proposed methods have not been evaluated in development processes. Most of the methods address a particular concern, or a few concerns, while there is a lack of a holistic approach.