The health care sector has become a large part of the national economy. Its expenditure share in the gross domestic product has been increasing over the years. An important piece of information for the current policy debate is the effectiveness and efficiency of our health care system. The objective of this study is to review and critique approaches in measuring the effectiveness and efficiency of health care production at the sub-sector level. For the market economy, economists identify three main type of efficiencies, namely, technical efficiency, cost efficiency, and allocative efficiency. A measure of efficiency, often called productivity, is the amount of output produced by a unit of input. For reasons of social equity and the market structure and incentives, most developed countries choose a publicly funded health care system. The output quantity of health care services is a key component in productivity measurement. There are, however, conceptual difficulties in pinpointing a precise definition in health care output. Current practices include factor inputs, service activities, course of treatment, health status of patients, and monetary metric of overall well-being. Lack of observed output prices further adds to the challenge of aggregating different services into a higher level index number. There are two general approaches in measuring productivity change over time. The statistical approach is more flexible and versatile but technically more challenging. The index number approach requires more assumptions on the production technology. The benefits are simplicity, ease of use, and consistency of the results. For efficiency comparison across regions or production units, analysts have developed the data envelopment technique in addition to statistical and index number approaches. All three methods are based on a concept called the Malmquist productivity index. Data envelopment analysis is also a flexible and versatile technique, with minimal assumption on the production technology. The method is popular among health care analysts and managers. There are, however, a few technical deficiencies and shortcomings. Other practical challenges facing health care analysts are consistent in output definitions, the treatment of quality changes in the services, and the lack of appropriate input data for productivity calculation.