This paper provides a comprehensive review of the latest advancements in fetal motion correction in MRI. We delve into various contemporary methodologies and technological advancements aimed at overcoming these challenges. It includes traditional 3D fetal MRI correction methods like Slice to Volume Registration (SVR), deep learning-based techniques such as Convolutional Neural Networks (CNNs), Long Short-Term Memory (LSTM) Networks, Transformers, Generative Adversarial Networks (GANs) and most recent advancements of Diffusion Models. The insights derived from this literature review reflect a thorough understanding of both the technical intricacies and practical implications of fetal motion in MRI studies, offering a reasoned perspective on potential solutions and future improvements in this field.