**4. Conclusion**

Classifying national health systems has been a need of researchers to order and study the diversity of the observed reality. In the last 30 years, the European health systems have been classified according to several criteria which generated a set of different typologies. In this article, the most relevant typologies are presented. Six non-analytical typologies are presented. These typologies' main differentiating factor is the number and the type of criteria used to deduce and describe the group of health systems. More sophisticated typologies are also presented in the period 2000–2015. These are based on statistical analysis and produce groups of countries which share common statistical traits based on how similar health systems are to each other and different from others. Three well-known typologies of this kind are referred.

The majority of typologies proposed and presented here is based on a descriptive and/or qualitative analysis of health systems. While this method is like filling in a line or matrix of criteria, it is more susceptible to criticism, in particular, from each country expert when comparing countries. Moreover, most of these typologies do not cover a wide range of European countries, preventing any potential comparison.

Recently, the increase of data availability and computer capacity to perform statistical analysis has motivated researchers to look for more objective and sophisticated typologies. Cluster analysis has been used to construct and propose three different typologies presented here. This type of statistical method is based on an algorithm aimed at identifying groups of countries that are similar to each other but different from countries in other groups. The key instrument to measure that similarity is the Euclidean distance. The results depend not only on the number and set of countries but also on the characterizing variables considered. For this reason, each typology is internally valid for a period/year, set of countries, and variables considered.

The most used criterion is financing which clearly reflects the central concern placed on this feature. Financing may be seen as a base of the health system functioning and where all the other functions are standing on. From this point of view, there is a consensual view that health systems may be dominantly Beveridgean, Bismarckean, mixed, or private type. While some countries may show some consistency over time, some countries do change their funding process along time. Future research may focus on how and why changes have occurred and what were the effects on the population health of such changes.

The second most used criterion is provision and delivery. Not only, these functions may be proxied and compared easily with data across countries; they also convey information about the functioning of the health system. The delivery/provision of health care is crucial to improve population health results and performance assessment. The ideas behind this function may be differentiated into access, availability, utilization, and coverage of health care. It is likely that future typologies, in particular, when considering similar health systems, will look for variables that may proxy each of these facets of provision.

Finally, it is worth to notice that authors seem pleased to baptize each group of countries in a typology. Except for those typologies based on the criteria of financing, where some agreement exists for the given names, the remaining typologies present different and creative labels for the groups found. This fact reflects the lack of comparability across typologies. Nevertheless, some researchers may found interesting to analyze the typologies for a single country, a long time, since it provides a multiple view of the health system along time.
