The main question that guides this paper is how governments are focusing (and must focus) on competence building (education, training and skills) when designing and implementing innovation policies. After a brief literature review, this paper suggests a typology of internal/external and individual/organizational sources of competences that are related to innovation activities. This serves to examine briefly the most common initiatives that governments are taking in this regard. The paper identifies three overall deficiencies and imbalances in innovation systems in terms of education, training and skills: the insufficient levels of competences in a system, the time lag between firms’ short-term needs for specific competences and the long time required to develop them, and the imbalances between internal and external sources of competences in firms. From these, the paper elaborates a set of overall criteria for the (re)design of policy instruments addressing those tensions and imbalances.