The group Waves in complex systems in Nice (France) is interested in controlling the wave transport properties in various systems whose mastered designs range from homogeneous systems with complex geometries to either (quasi-)periodic or disordered structured materials. Thanks to a versatile experimental platform in the microwave domain, we addressed in the last years the vivid field of topological physics/photonics, and obtained different results ranging from the concept of topological reflective limiter, to a physical interpretation of the gap-labelling in a Penrose tilling, not forgetting the observation of a topological phase transition in strained artificial graphene. During the colloquium, I will give a simple introduction of topological physics, describe the experimental platform, and present a selection of results.