Labour markets are currently in a phase of cyclical recovery and undergoing structural transformation due to globalisation, demographic trends, advancing digital technologies and automation and changes in labour market institutions. Against this background, businesses increasingly report that the limited availability of skills poses an impediment to corporate investment. Genuine skill constraints can negatively affect labour productivity and hamper the ability to innovate and adopt technological developments. For individual Europeans, not having ‘the right skills’ limits employability prospects and access to quality jobs. For Europe at large, persistent skill gaps and mismatches come at economic and social costs. This paper reviews the recent economic literature on skill mismatch and skill shortages with a focus on Europe.