This paper focuses on classifying market access for long-distance passenger rail services in Europe into three main models and discusses the advantages and disadvantages of each of these models. The "Tendered Concessions" model aims to introduce competition for the market by which operators are selected in a tendering procedure. The "Monopolistic Network Operator" model aims to sustain network effects by granting a concession to one operator. The "Open Market" model enhances operators' entrepreneurship by providing opportunities to plan services based on open access to the network. We present the strengths and opportunities, risks and threats without favoring any one model. Classifying the many design options and their different impacts will help to structure the ongoing policy discussion. The paper also gives an overview of the organization of long-distance passenger railway markets in selected European countries, and discusses the development of Germany's longdistance rail passenger services in particular.