Homeopathy is the subject of frequent debates, especially in public media. This systematic review aims to give an overview of conceptual criticisms of homeopathy in the scientific literature. The literature search was conducted in four databases (EMBASE, PubMed, Web of Science, PhilPapers) on August 25, 2020. Included were peer reviewed articles in English or German criticising the basic concepts of homeopathy as main topic; excluded were articles criticising homeopathy primarily based on analysis of empirical clinical and/or preclinical data. The formal structure of publications included was evaluated regarding the recommended structure for scientific publications (IMRaD, acronym for ‘Introduction’, ‘Methods’, ‘Results’ and ‘Discussion’). Arguments criticising the concepts of homeopathy were extracted and classified into groups. The literature search revealed 5139 articles, of which 15 articles (published between 1959 and 2020) met the inclusion criteria. These articles complied only partly with the IMRaD structure; just four articles considered with 8 or 9 IMRaD criteria the majority of the defined 11 IMRaD criteria. Extracted arguments against the concepts of homeopathy were classified into five groups: ‘Conflict with current scientific principles and the foundations of modern medicine’, ‘Lack of a scientific basis’, ‘Arguments based on scientific theories’, ‘Ethical considerations and social consequences’, ‘Lack of empirical clinical evidence’. This classification is intended to provide a basis for future in-depth scientific analyses and discussions. Based on the number of articles found in the peer reviewed literature, it can be concluded that the on-going discussion about homeopathy in the public media is not reflected in a corresponding academic debate.