Order, regularities, and patterns are ubiquitous around us. A flock of birds maneuvering in the sky, the self-organization of social insects, a global pandemic or a traffic jam are examples of complex systems where the macroscopic patterns arise from the microscopic interaction of individual agents. Not only is the study of complex systems an important domain on its own but also represents a "powerful idea" that cuts across disciplines and can lead to the understanding of a large class of physical and social phenomena. Swarm robotics is a field within robotics that models the collective behavior of decentralized and self-organized systems, primarily inspired by social insects in nature. The adaptability, scalability and resilience of swarm robots make them an appealing solution for a wide array of problems and applications across scales including search and rescue missions, large-scale logistics, environmental monitoring, entertainment and nanomedicine. A promising yet under-explored area is education. In this thesis, we investigate a novel approach to learning with swarms, about swarms. We design, implement, and validate a comprehensive framework that can be used in formal as well as informal educational settings to foster understanding of complex systems. This includes the creation of an assessment instrument to measure complex systems understanding, the development of a platform for users to interact with multiple virtual as well as robotic agents, and the design and implementation of learning activities and educational games. These components are validated with experimental studies and analyses. We conducted a series of experiments with a total of over 200 participants spanning different age groups from high school students to adults. Our primary activity, named Cellulan World, designed as an individual human-swarm interaction game, demonstrated significant positive learning gains in complex systems understanding, as well as high reported engagement and enjoyment. The experiments also revealed interesting insights into the learning process and the user interaction aspects. Furthermore, we explore group activities in a "double swarm" setting where multiple humans interact with multiple robots. We delve deeper into the agent-agent interaction, focusing on different communication affordances, such as local and global verbal communication, as well as visual and haptic non-verbal communications. In the context of this thesis, we re-designed the educational table-top swarm robot Cellulo, originally conceived in our lab, to allow for a modular architecture and broaden the scope of interaction with the robot. Simultaneously, we developed a library for our robotic platform using the cross-platform Unity game engine, simplifying the design and development of activities and games involving both humans and individual or swarms of robots. This also allows for the seamless integration of tangible and virtual elements. By offering an innovative and engaging educational experience, our framework presents a promising avenue to foster understanding and appreciation of the fascinating world of complex systems.