Fetal development is a critical phase in prenatal care, demanding the timely identification of anomalies in ultrasound images to safeguard the well-being of both the unborn child and the mother. Medical imaging has played a pivotal role in detecting fetal abnormalities and malformations. However, despite significant advances in ultrasound technology, the accurate identification of irregularities in prenatal images continues to pose considerable challenges, often necessitating substantial time and expertise from medical professionals. In this review, we go through recent developments in machine learning (ML) methods applied to fetal ultrasound images. Specifically, we focus on a range of ML algorithms employed in the context of fetal ultrasound, encompassing tasks such as image classification, object recognition, and segmentation. We highlight how these innovative approaches can enhance ultrasound-based fetal anomaly detection and provide insights for future research and clinical implementations. Furthermore, we emphasize the need for further research in this domain where future investigations can contribute to more effective ultrasound-based fetal anomaly detection.