Ensuring safety in human–robot collaboration is one of the main challenges in mobile robotics today. Semantic maps are a potential solution because they provide semantic knowledge in addition to the geometric representation of the environment. They allow robots to perform their basic tasks using geometric representation, mainly localization, path planning and navigation, and additionally allow them to maintain a cognitive interpretation of the environment in order to reason and make decisions based on the context. The goal of this paper is to briefly review semantic mapping for a single mobile robot in indoor environments, and then focus on collaborative mobile semantic mapping. In both contexts, the semantic mapping process is divided into modules/tasks, and recent solutions for each module are discussed. Possible system architectures are also discussed for collaborative semantic mapping. Finally, future directions are highlighted.