Cardiovascular neurocristopathy is associated with abnormal migration and development of neural crest cells, impacting the neural and the human cardiovascular system and leading to diseases such as cardiomyopathy, aortic disease, and aortic valve dysfunction. With advancements in biomedical imaging tools, efforts are made to understand the underlying causes of cardiovascular neurocristopathy and develop new diagnostic methods, especially using machine learning or specifically its sub-branch deep learning models. This article provides a systematic survey of the literature related to machine/deep learningbased segmentation of the diseases mentioned above in computer tomography (CT), magnetic resonance imaging (MRI), X-rays, and echocardiogram (Echos) images. The review identified gaps and provides future directions, such as the need for better interpretable and explainable AI models, addressing the lack of publicly available datasets, standardizing the result reporting procedure for better repeatability of the result, and the development of standard performance measurement metrics. The general conclusion suggests that there is a need for multimodalities, multimodel, high-quality data sets, and open-source disease-specific dataspaces that will help develop trustworthy deep learning models that could be implemented in imaging devices/tools and provide medical-grade segmented outputs that will augment and speed up clinician decision making.