Cardio-cerebrovascular diseases are the leading causes of mortality worldwide, whose accurate blood vessel segmentation is significant for both scientific research and clinical usage. However, segmenting cardio-cerebrovascular structures from medical images is very challenging due to the presence of thin or blurred vascular shapes, imbalanced distribution of vessel and non-vessel pixels, and interference from imaging artifacts. These difficulties make manual or semi-manual segmentation methods highly time-consuming, labor-intensive, and prone to errors with interobserver variability, where different experts may produce different segmentations from a variety of modalities. Consequently, there is a growing interest in developing automated algorithms. This paper provides an up-to-date survey of deep learning techniques, for cardio-cerebrovascular segmentation. It analyzes the research landscape, surveys recent approaches, and discusses challenges such as the scarcity of accurately annotated data and variability. This paper also illustrates the urgent needs for developing multi-modality label-efficient deep learning techniques. To the best of our knowledge, this paper is the first comprehensive survey of deep learning approaches that effectively segment vessels in both the heart and brain. It aims to advance automated segmentation techniques for cardio-cerebrovascular diseases, benefiting researchers and healthcare professionals.