Placental segmentation is critical for the quantitative analysis of prenatal imaging applications. However, segmenting the placenta using magnetic resonance imaging (MRI) and ultrasound is challenging because of variations in fetal position, dynamic placental development, and image quality. Most segmentation methods define regions of interest with different shapes and intensities, encompassing the entire placenta or specific structures. Recently, deep learning has emerged as a key approach that offer high segmentation performance across diverse datasets. This review focuses on the recent advances in deep learning techniques for placental segmentation in medical imaging, specifically MRI and ultrasound modalities, and cover studies from 2019 to 2024. This review synthesizes recent research, expand knowledge in this innovative area, and highlight the potential of deep learning approaches to significantly enhance prenatal diagnostics. These findings emphasize the importance of selecting appropriate imaging modalities and model architectures tailored to specific clinical scenarios. In addition, integrating both MRI and ultrasound can enhance segmentation performance by leveraging complementary information. This review also discusses the challenges associated with the high costs and limited availability of advanced imaging technologies. It provides insights into the current state of placental segmentation techniques and their implications for improving maternal and fetal health outcomes, underscoring the transformative impact of deep learning on prenatal diagnostics.