Ultrasound offers a safe, cost-effective, and widely accessible technology for fetal brain imaging, making it especially suitable for routine clinical use. However, it suffers from view-dependent artifacts, operator variability, and a limited field of view, which make interpretation and quantitative evaluation challenging. Ultrasound compounding aims to overcome these limitations by integrating complementary information from multiple 3D acquisitions into a single, coherent volumetric representation. This work provides four main contributions: (1) We present the first systematic categorization of computational strategies for fetal brain ultrasound compounding, including both classical techniques and modern learning-based frameworks. (2) We implement and compare representative methods across four key categories - multi-scale, transformation-based, variational, and deep learning approaches - emphasizing their core principles and practical advantages. (3) Motivated by the lack of full-view, artifact-free ground truth required for supervised learning, we focus on unsupervised and self-supervised strategies and introduce two new deep learning based approaches: a self-supervised compounding framework and an adaptation of unsupervised deep plug-and-play priors for compounding. (4) We conduct a comprehensive evaluation on ten multi-view fetal brain ultrasound datasets, using both expert radiologist scoring and standard quantitative image-quality metrics. We also release the USFetal Compounding Toolbox, publicly available to support benchmarking and future research. Keywords: Ultrasound compounding, fetal brain, deep learning, self-supervised, unsupervised.