Catalytic swimmers self-propel by generating slip flows along their surface in response to physicochemical gradients in their environment resulting from their own chemical activity. Chemical patterning of these particles is the most classical route to break symmetry and achieve self-propulsion (e.g. Janus particles). Yet, experiments show that chemically-identical particles may propel in opposite directions, emphasising that chemistry alone may not be sufficient to fully determine their propulsion characteristics. In this presentation, we will show how the detailed particle geometry may profoundly influence their swimming direction and velocity, as well as the hydrodynamic interactions between particles. A brief overview of other routes to symmetry-breaking will also be presented for these particles.