The integration of the Internet of Things (IoT) with machine learning (ML) is revolutionizing how services and applications impact our daily lives. In traditional ML methods, data are collected and processed centrally. However, modern IoT networks face challenges in implementing this approach due to their vast amount of data and privacy concerns. To overcome these issues, federated learning (FL) has emerged as a solution. FL allows ML methods to achieve collaborative training by transferring model parameters instead of client data. One of the significant challenges of federated learning is that IoT devices as clients usually have different computation and communication capacities in a dynamic environment. At the same time, their network availability is unstable, and their data quality varies. To achieve high-quality federated learning and handle these challenges, designing the proper client selection process and methods are essential, which involves selecting suitable clients from the candidates. This study presents a comprehensive systematic literature review (SLR) that focuses on the challenges of client selection (CS) in the context of federated learning (FL). The objective of this SLR is to facilitate future research and development of CS methods in FL. Additionally, a detailed and in-depth overview of the CS process is provided, encompassing its abstract implementation and essential characteristics. This comprehensive presentation enables the application of CS in diverse domains. Furthermore, various CS methods are thoroughly categorized and explained based on their key characteristics and their ability to address specific challenges. This categorization offers valuable insights into the current state of the literature while also providing a roadmap for prospective investigations in this area of research.