The rapid advancement of technology and the spread of Artificial Intelligence (AI) across various sectors of society are reshaping our daily lives and imply a series of emerging challenges. Given this fact, it is vital to detect and diagnose the nature of these challenges at an early stage, adopting a proactive approach to the design, development, and evaluation of AI systems; an ethics-by-design approach permeating all research phases. The challenges posed by the widespread use of AI systems impact the research ethics review process, which aims to ensure ethical and responsible research practices. Therefore, it is urgent to understand the effect of AI in the research area, along with the arising social implications, in order to increase the effectiveness of the research ethics review process for achieving more ethical AI research outcomes. This study aims to identify challenges related to the use of AI technologies across different sectors and to detect if and how these challenges impact research ethics and the research ethics review process. For this purpose, a systematic literature review was conducted. The initial findings of this review facilitated the creation of a classification framework, which provides a structured basis for in-depth research. The proposed framework is based on the assumption that identifying and categorising the arising challenges can enable more effective ways to address them. Thus, future policies to meet these challenges can be more targeted and impactful. This study highlights the need for further research, including a deeper and more extensive literature review in the field, as well as empirical validation of the classification framework through qualitative feedback from members of Research Ethics Committees (RECs).