The principle design idea of C-RAN is to move some of RAN functionalities to the cloud infrastructure, the BBU pool could be implemented on a cloud platform [4]. The path towards O-RAN making mobile networks \"more software driven, virtualized, flexible, intelligent and energy efficient\", as well as \"cost-efficient and reliable\" [2], is paved through the use of Network Function Virtualization (NFV) concepts. The O-RAN concept is supported by several standard bodies such as the O-RAN Alliance [5], the Third Generation Partnership Project (3 GPP) [6], the European TelecommunicationsStandards Institute (ETSI) [7], the Next Generation Mobile Networks (NGMN) [8], and the Optical Internetworking Forum (OIF) [9], to ensure interoperability and interconnection between O-RAN components from different vendors. As O-RAN environments are inherently complex, characterized by heterogeneity and dynamism, with various hardware and software components from different vendors working together, Machine Learning (ML) is expected to be an invaluable tool. The effectiveness and efficiency of O-RAN architectures are intricately tied to the integration of ML capabilities. ML techniques offer a plethora of advantages within O-RAN architectures. ML algorithms excel at real-time analysis of extensive network data, including KPIs, end-user behaviors, and network traffic patterns, all in real-time. This analytical strength empowers the prompt identification of trends, anomalies, and performance issues, facilitating network optimization and predictive maintenance [10]. Moreover, ML plays a vital role in resource allocation by intelligently assigning radio resources, optimizing resource utilization, and enhancing QoS [11]. Additionally, ML algorithms facilitate data-driven decision-making in O-RAN management and orchestration functions, such as automated network configuration, dynamic spectrum allocation, and intelligent traffic steering. This streamlined approach reduces network management complexity and empowers MNOs to optimize network performance. Overall, ML is a very important tool for O-RAN as it allows for the provision of insights, efficient resource allocation, and automated management capabilities. In this paper, we embark on a comprehensive exploration of the current landscape concerning ML applications in O-RAN. Our objective is to identify and analyze the prevailing challenges that remain unresolved, preventing the full harnessing of ML's potential for enhancing O-RANs. While there have been several O-RAN survey papers in the literature [1; 4; 12; 13; 14; 15; 16; 17; 18; 19], our survey paper stands out as it concentrates on the applications and potential of ML within the O-RAN context, which has not been extensively addressed in prior surveys. Table 1 provides a summary of the topics covered in relevant surveys, along with their contributions, in order to provide a clear comparison with our work. It can be noted that most of the existing surveys aim to provide a detailed tutorial on RAN evolution, O-RAN architecture, and components and use cases. They all have different focuses compared to our paper. For example, ref. [16] specifically focuses on the security and privacy risks associated with Open RAN architecture, which complements our survey. Meanwhile, ref. [17] centers its attention on the Non-Terrestrial Network (NTN), offering an architectural solution for an O-RAN-based NTN system. In addition, although [18; 19] both acknowledge the prevailing challenges and prospective research directions in this field, ref. [18] primarily examines the existing O-RAN specifications, while [19] focuses on how Explainable AI (XAI) can contribute to O-RAN networks. Among the existing survey papers, refs. [14; 15] have a similar focus on ML in O-RAN. Ref. [14] mainly provides a tutorial on how intelligent applications can improve the efficiency of O-RAN and the future opportunities in O-RAN, while [15] looks into how deep learning solutions can be integrated to the O-RAN architecture, as well as case studies. However, ref.