The vascular network in the human body is characterized by blood vessels exhibiting drastic structural variations in radius, length, topological properties, and branching patterns. This heterogeneity, together with location-specific anatomical background variations, poses a significant challenge for robust, large-scale analysis of the entire cardiovascular system. As a result, most research has focused on narrow, isolated segments of the vascular network. While such targeted studies provide valuable insights, they inherently limit the ability to assess the systemic health and functional integrity of the vascular network as a whole. In this work, we aim to bridge this gap to advance both clinical diagnostics and our fundamental understanding of vascular physiology. We propose the task of segmenting all vessels in CT images, ranging from the largest components of the cardiovascular system to even minuscule mesenteric vessels. To this end, we introduce vesselFM-CT, the first model capable of robustly segmenting all blood vessels in 3D CT images. VesselFM-CT is trained via an iterative, multi-step process and optimizes our proposed TubeLoss loss function, effectively addressing the inherent heterogeneity of the cardiovascular system. We demonstrate that vesselFM-CT outperforms all baselines and enables automated, precise extraction of the cardiovascular system from CT images, thereby unlocking a wide range of clinical and technical perspectives, including automated disease classification and synthetic CT image generation.