Digitalization is currently gaining wide scope not only in the EU but also throughout the world. The main reason for this, in addition to improving technology, is also the COVID-19 pandemic period, which played an integral role in the faster transition to digitalization. This process is also widely reflected in the field of copyright law. The digitalization of copyrighted works including text, music and video has dramatically increased the efficiency of unauthorized copying. It becomes easier to copy and share digital information, to copy and paste from a web page, to share files. Subsequently, governmental bodies focused on the effective regulation of copyright law in the digital market (DM). The gradual advancement in digitalization and the empowerment of less expensive and affordable use of copyrighted objects have led to the adoption of the Directive 2019/790 of the European Parliament and of the Council of 17 April 2019 on copyright and related rights in the Digital Single Market (DSM Directive), which is the most striking precedent in the field of digital copyright law.With the gradual transition of these legal relations to a still poorly studied digital single market (DSM), the regulation of copyright law in DM and the identification of facts of copyright infringement become more complicated. To alleviate the current situation, the concept of copyright infringement, methods of infringement and its legislative and practical consequences within the framework of European Union (EU) law, as well as a brief analysis of the Court of Justice of the European Union’s (CJEU) decisions are considered. The concept and methods of copyright infringement give rise to consideration of copyright holders’ rights under the DSM Directive. Copyright has a rather deep history of origin and formation, therefore, consideration of all rights under copyright is not the focus in this thesis, but only the rights that are specifically protected and used with the transition to the DM. It is especially important to note Articles 15 and 17 of the DSM Directive, which have been criticized for the primary provisions. This attitude towards an entirely new piece of legislation undermined the credibility of its implementation by the EU Member States. This harsh criticism led to certain changes.It is also worth exploring current challenges and new approaches to the copyright law in DM, specifically balancing the freedom of expression and copyright law, as well as the effect of the COVID-19 pandemic on digital copyright law.The purpose of this paper is to research copyright law infringement and protection of rights of copyright holders in DM under DSM Directive. It is aimed at analysing the concept of copyright infringement in DM, CJEU’s assessment of copyright infringements in DM under EU law and whether the rights of copyright owners in DM are protected properly. The ambition for this research is settled narrowly in the fact of increasing digitalisation in the field of copyright law, specifically copyrighted works in social media, and current challenges in the regulation of DSM within the EU.The following research questions will be answered in order to achieve the purpose of this paper:1. How is the copyright law regulated in DM?2. What is copyright infringement in DM?3. What are the methods of copyright infringement in DM?4. What is the role of individual users and intermediaries in copyright infringement in DM?5. What are the most criticized provisions of the DSM Directive? Why?6. How is the freedom of expression and COVID-19 pandemic counted as emerging challenges of digital copyright law?Since the topic is broad and can cover different fields of law, the following delimitations have to be made. The main focus of this work is EU copyright law which can be eventually narrowed down on focusing on copyright infringement, rights of copyright holders and protection measures. As copyright law is a quite broad and well-researched field of law, the work is limited to the extent of the DM within the EU. Moreover, rights under copyright law will be concerned only in regards to the DM, and a limited number of rights will be discussed. This thesis will not broadly analyse the rights of copyright holders other than that can be concerned in DM.This thesis will not go into detail about the DSM and will limit with a general overview of it in order to make clear what the concept of DSM is. There are several research methods used in this thesis, one of which is descriptive research. Descriptive research, as its name suggests, describes the state of affairs as it exists at present and it merely describes the phenomenon or situation under study and its characteristics. The analysis of copyright infringement concept, DSM concept and protection of rights of copyright owners have been concerned via this type of methodology. The second method is applied research or action research, which aims at discussing and finding a solution for an immediate problem. This method involves rising problematic issues and immediate ways of their solution. The applied research method can be seen in chapters 4 and 5 of this paper in regard to practical challenges under digital copyright law. The third legal research method applied in this paper is comparative research and the EU-legal method. This type of research crosses traditional categories of law, integrating public and private international law with domestic law, European law and the comparative method. Moreover, the EU law, Regulations and Directives have an indispensable role in formulating the analysis of copyright law in DM. This method also considers practical and case law approach to the analysis, where previous cases of CJEU and other courts are referred to make a deep comparison within the applied field of law. Both sources of EU law, primary and secondary sources, are included in the used material of this thesis. Primary sources in this thesis include the EU legislation, as well as legal instruments concerning Copyright Law in the EU legal system, the case law of CJEU.Secondary sources in this thesis include books, academic articles, Advocate General’s opinions, doctrinal works, legal blog sources and commentaries on the applied field in this thesis. This thesis consists of six chapters. In the introductory chapter, the problem, overview and methodology of the thesis research are addressed.The second chapter named Copyright law and Digitalization refers to the understanding of concepts of copyright law, copyright infringement and DSM under EU law. The chapter also refers to the DSM Directive and explains the role of this Directive in the regulation of copyright law in DM.The third chapter introduces the analysis of copyright infringement in DM which is concerned with the theoretical and practical approaches. This chapter provides an in-depth analysis of copyright infringement with its methods, latest examples and case law, as well as takes individual infringers and intermediaries as subjects of copyright infringement.The fourth chapter focuses on the DSM Directive and its role in the protection of copyrighted works. It also discusses Articles 15 and 17 of this Directive and defines their role in the protection of the rights of copyright holders.The fifth chapter focuses on current challenges in copyright law in the digital world. This chapter considers the balance between freedom of expression and copyright, as well as the effect of the COVID-19 pandemic as important challenges.Finally, the concluding chapter makes an overall review of the analysis in this thesis and also refers to possible solutions of raising questions