**1. Introduction**

European countries display diversified arrangements to provide health care, to finance, and to cover health insurance expenditures. These organized arrangements constitute the health system of each country.

The definition of health system has evolved over time since Alma Ata Declaration in 1978 [1]. Several definitions have been proposed, either by single authors (such as Weinerman [2] and Long [3]) or by institutions (such as the World Bank [4] and WHO [5]).

The most widely accepted definition was published in 2007 in the report "Everybody's business: strengthening health systems to improve health outcomes: WHO's framework for action, 2007" [6]. The definition of health system here is given as "a system of all organizations, people and actions whose primary intentions are to promote, restore or maintain health," which includes efforts to influence determinants of health, as well as more direct health-improving activities.

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The WHO definition implicitly considers the goals of a (national) health system. These goals are both final and intermediate [7]. The final goals of a health system are responsiveness to people's expectations, social and financial risk and fair protection, and improved health; the intermediate goals on their turn are improving access, improving coverage, delivering high quality and safe health services, promoting healthy behavior, and improving efficiency.

These goals justify the functions of health systems themselves. The WHO [5] proposes four functions of a health system which are (i) health service provision, (ii) health generation of resources (investment and training), (iii) stewardship, and (iv) health financing (collecting, pooling, and purchasing). The functions of the health systems may be described as follows:

(i) The *provision* (*also referred as delivery*) of health-care services which requires the management of resources and the creation of human resources, delivery of medications, medical services, and medical equipment.

(ii) The *generation of resources* which implies not only their management, but also their creation. While some inputs may be gathered in short term after the investment, other resources may take a long time to obtain and train as the human resources.

(iii) *Stewardship* or overall system oversight which sets the context and policy framework for the overall health system. This function is usually (but not always) a governmental responsibility, where the health priorities, the institutional framework, the activities that should be coordinated with other systems, and the information needed to support the decision-making process are set.

(iv) *Financing or funding* which includes collecting revenues, pooling financial risk, and allocating revenue. (a) The collection of revenue may be done in different ways, and it includes general taxation, donor financing, mandatory payroll contributions, mandatory or voluntary risk-rated contributions (premiums), direct household out-of-pocket expenditures, and other forms of personal savings. (b) Risk pooling refers to the management of financial resources in order to spread the risk from an individual to the pool of individuals, reducing in this way the overall risk for the system. (c) Strategic purchasing or financing of the supply side means the way providers and purchasers establish an interaction and develop service delivery models.

The functions of the health system have been used as dimensions or criteria of classification of health systems. Most traditional criteria used are proxies of financing and delivery functions. But other criteria have been used to capture features of resource generation and stewardship, such as health system actors, cost-sharing, medical technology, and decentralization. Several typologies have been proposed in the last 30 years; some are simple and based on a single criterion, and others are more complex and based on statistical analysis.

The aim of this work is to review the most influential typologies created in the last 30 years to classify the European health systems. The different typologies are summarized, and their most significant features are presented. The contribution of this article is mainly of twofold. On the one hand, it provides a synthesized historical review of how national health systems have been studied over time in Europe; on the other hand, it allows for the possibility to easily describe, criticize, and analyze the evolution of a single health system in the last 30 years.

Additionally, the implicit purpose of this work is to provide an informative and friendly view on how different authors have positioned European health systems in a criteria line or matrix. Some other works in the literature may devote some paragraphs to this theme, but no work is exclusively dedicated to the historical review of health system typologies. These typologies, which are considered as the most influential, were found after a literature review and scholar Google search based on the terms "health system classification"/"health system typologies."
