The segmentation of liver blood vessels is of major importance as it is essential for formulating diagnoses, planning and delivering treatments, as well as evaluating the results of clinical procedures. Different imaging techniques are available for application in clinical practice, so the segmentation methods should take into account the characteristics of the imaging technique. Based on the literature, this review paper presents the most advanced and effective methods of liver vessel segmentation, as well as their performance according to the metrics used. This paper includes results available for four imaging methods, namely: computed tomography (CT), computed tomography angiography (CTA), magnetic resonance (MR), and ultrasonography (USG). The publicly available datasets used in research are also presented. This paper may help researchers gain better insight into the available materials and methods, making it easier to develop new, more effective solutions, as well as to improve existing approaches. This article analyzes in detail various segmentation methods, which can be divided into three groups: active contours, tracking-based, and machine learning techniques. For each group of methods, their theoretical and practical characteristics are discussed, and the pros and cons are highlighted. The most advanced and promising approaches are also suggested. However, we conclude that liver vasculature segmentation is still an open problem, because of the various deficiencies and constraints researchers need to address and try to eliminate from the solutions used.