While the topic of artificial intelligence (AI) in multinational enterprises has been receiving attention for some time, small and medium enterprises (SMEs) have recently begun to recognize the potential of this new technology. However, the focus of previous research and AI applications has therefore mostly been on large enterprises. This poses a particular issue, as the vastly different starting conditions of various company sizes, such as data availability, play a central role in the context of AI. For this reason, our systematic literature review, based on the PRISMA protocol, consolidates the state of the art of AI with an explicit focus on SMEs and highlights the perceived challenges regarding implementation in this company size. This allowed us to identify various business activities that have been scarcely considered. Simultaneously, it led to the discovery of a total of 27 different challenges perceived by SMEs in the adoption of AI. This enables SMEs to apply the identified challenges to their own AI projects in advance, preventing the oversight of any potential obstacles or risks. The lack of knowledge, costs, and inadequate infrastructure are perceived as the most common barriers to implementation, addressing social, economic, and technological aspects in particular. This illustrates the need for a wide range of support for SMEs regarding an AI introduction, which covers various subject areas, like funding and advice, and differentiates between company sizes.