Plasma catalysis is gaining increasing interest for various gas conversion applications, such as CO2 conversion into value-added chemicals and fuels, CH4 activation into hydrogen, higher hydrocarbons or oxygenates, and NH3 synthesis. Other applications are already more established, such as for air pollution control, e.g. volatile organic compound remediation, particulate matter and NOx removal. In addition, plasma is also very promising for catalyst synthesis and treatment. Plasma catalysis clearly has benefits over 'conventional' catalysis, as outlined in the Introduction. However, a better insight into the underlying physical and chemical processes is crucial. This can be obtained by experiments applying diagnostics, studying both the chemical processes at the catalyst surface and the physicochemical mechanisms of plasma-catalyst interactions, as well as by computer modeling. The key challenge is to design cost-effective, highly active and stable catalysts tailored to the plasma environment. Therefore, insight from thermal catalysis as well as electro- and photocatalysis is crucial. All these aspects are covered in this Roadmap paper, written by specialists in their field, presenting the state-of-the-art, the current and future challenges, as well as the advances in science and technology needed to meet these challenges.