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In recent years, a variety of segmentation methods have been proposed for automatic delineation of the fetal and neonatal brain MRI. These methods aim to define regions of interest of different granularity: brain, tissue types or more localised structures. Different methodologies have been applied for this segmentation task and can be classified into unsupervised, parametric, classification, atlas fusion and deformable models. Brain atlases are commonly utilised as training data in the segmentation process. Challenges relating to the image acquisition, the rapid brain development as well as the limited availability of imaging data however hinder this segmentation task. In this paper, we review methods adopted for the perinatal brain and categorise them according to the target population, structures segmented and methodology. We outline different methods proposed in the literature and discuss their major contributions. Different approaches for the evaluation of the segmentation accuracy and benchmarks used for the segmentation quality are presented. We conclude this review with a discussion on shortcomings in the perinatal domain and possible future directions.We present a comprehensive review of perinatal brain MRI segmentation methods.A detailed classification of techniques is proposed based on methodology.We outline existing atlases for the fetal and neonatal brain.We discuss future directions and open challenges for research.