Robot swarms are groups of robots that each act autonomously based on only local perception and coordination with neighboring robots. While current swarm implementations can be large in size (e.g., 1,000 robots), they are typically constrained to working in highly controlled indoor environments. Moreover, a common property of swarms is the underlying assumption that the robots act in close proximity of each other (e.g., 10 body lengths apart), and typically employ uninterrupted, situated, close-range communication for coordination. Many real world applications, including environmental monitoring and precision agriculture, however, require scalable groups of robots to act jointly over large distances (e.g., 1,000 body lengths), rendering the use of dense swarms impractical. Using a dense swarm for such applications would be invasive to the environment and unrealistic in terms of mission deployment, maintenance and post-mission recovery. To address this problem, we propose the sparse swarm concept, and illustrate its use in the context of four application scenarios. For one scenario, which requires a group of rovers to traverse, and monitor, a forest environment, we identify the challenges involved at all levels in developing a sparse swarm—from the hardware platform to communication-constrained coordination algorithms—and discuss potential solutions. We outline open questions of theoretical and practical nature, which we hope will bring the concept of sparse swarms to fruition.