In swarm robotics multiple robots collectively solve problems by forming advantageous structures and behaviors similar to the ones observed in natural systems, such as swarms of bees, birds, or fish. However, the step to industrial applications has not yet been made successfully. Literature is light on real-world swarm applications that apply actual swarm algorithms. Typically, only parts of swarm algorithms are used which we refer to as basic swarm behaviors. In this paper we collect and categorize these behaviors into spatial organization, navigation, decision making, and miscellaneous. This taxonomy is then applied to categorize a number of existing swarm robotic applications from research and industrial domains. Along with the classification, we give a comprehensive overview of research platforms that can be used for testing and evaluating swarm behavior, systems that are already on the market, and projects that target a specific market. Results from this survey show that swarm robotic applications are still rare today. Many industrial projects still rely on centralized control, and even though a solution with multiple robots is employed, the principal idea of swarm robotics of distributed decision making is neglected. We identified mainly following reasons: First of all, swarm behavior emerging from local interactions is hard to predict and a proof of its eligibility for applications in an industrial context is difficult to provide. Second, current communication architectures often do not match requirements for swarm communication, which often leads to a system with a centralized communication infrastructure. Finally, testing swarms for real industrial applications is an issue, since deployment in a productive environment is typically too risky and simulations of a target system may not be sufficiently accurate. In contrast, the research platforms present a means for transforming swarm robotics solutions from theory to prototype industrial systems.