The growth of health care needs and the hospital establishment capacity has led to increased costs together with a deterioration in the finances of national health public systems. Hospitals need to understand how they can improve efficiency and service quality to survive and keep on operating with a sustainable activity for the future. Hospitals have to face hard budget constraints and on the other side maintain a high quality of care and improved health outcomes. The hospital production is a topic that the microeconomists analyzed in the last fifty years, looking at the hospital efficiency able to provide the best outputs and outcomes using limited number of inputs. The modelling of this function was mostly performed using parametric methods (such as Translog and Cobb-Douglas functional forms or Stochastic Frontiers), and later with non-parametric methods (such as Data Envelopment Analysis). The objective of this preliminary study consists in providing an overview of the economic evaluation of hospital production, comparing the two methods and showing the main benefits and limitations of each approach.