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Accurate foetal ultrasound (US) image segmentation facilitates advanced obstetric health care by enabling remote monitoring of expectant mothers. However, foetal US image segmentation is challenging due to distortions, motion artefacts, various imaging conditions and presence of maternal anatomy. Recent research work has proposed many methods towards increasing the accuracy of foetal US image segmentation. This paper reviews 2D and 3D foetal US image segmentation methods under four main categories; deep learning-based method, machine learning-based methods, active contour-based methods and thresholding-based methods. Each of these methods are discussed highlighting their advantages, limitations and potential in contributing to further development. In addition, the paper highlights possible prospects that would streamline the future research work.