The Greek economy has so far failed to shift its production structure towards more complex, high value-added activities incorporating knowledge-intensive practices. Greece lacks a systemic "activating knowledge" dimension. Given the country's low performance in innovation and knowledge diffusion relative to EU peers, we focus on two specific problem areas of Greek industry: skills and management practices. Both areas are key requirements to achieve robust productivity growth, in which Greece has been shown to be chronically lagging behind its peers. First, we provide an in-depth look at skills indicators to identify the scope for action, particularly in addressing mismatch. A novel result is that, by utilising mismatch indicators aggregated from microdata sourced from the recent OECD Survey of Adult Skills that was conducted as part of the Programme for the International Assessment of Adult Competencies (PIAAC), we show that Greece has the highest overskilling for professional occupations. We also corroborate previous findings about the negative relationship between skills mismatch and firm productivity. Second, we use firm-level data from the World Management Survey to give a review of management practices in Greek industry and explore the quality of these practices and their association with productivity. Finally, we use information from a novel survey on entrepreneurship, technological developments and regulatory change, and examine the structural characteristics of Greek firms that innovate and tend to adopt new technologies, with a focus on the role of size, ownership structure, global value chain participation and human resource practices. Our empirical findings provide valuable input into concrete policy proposals to increase productivity in Greek manufacturing.