Employability is on the agenda. Yet, we lack the institutional structures and mechanisms to effectively promote it. Most of our labour institutions are at the national level on the one hand, on the industrial and company level on the other hand. Collective bargaining, for example, is typically geared to industries and companies. For the interindustrial or intersectoral levels we have some national forums, but no effective intermediate institutions and mechanisms. In our view, the phenomenon of the covenant may fill the gap. Covenants are an effective way of combining the public interest in enhanced employability, and the collective interests of employers and employees in an adequate, educated and 'empowered' labour force. Against the background of the needs of a 'knowledge economy' and the underinvestment in skills, in particular due to a one-sided 'flexibility' of the labour market, we first sketch the ambitions of the EU, and the present state and the shortcomings of the training efforts in the economy. Next, we explain what the covenant stands for, what its promises are for triggering more training and strengthening employability, and what role the critical issue of trusting co-operation is expected to play.