There is no denying how machine learning and computer vision have grown in the recent years. Their highest advantages lie within their automation, suitability, and ability to generate astounding results in a matter of seconds in a reproducible manner. This is aided by the ubiquitous advancements reached in the computing capabilities of current graphical processing units and the highly efficient implementation of such techniques. Hence, in this paper, we survey the key studies that are published between 2014 and 2020, showcasing the different machine learning algorithms researchers have used to segment the liver, hepatic-tumors, and hepatic-vasculature structures. We divide the surveyed studies based on the tissue of interest (hepatic-parenchyma, hepatic-tumors, or hepatic-vessels), highlighting the studies that tackle more than one task simultaneously. Additionally, the machine learning algorithms are classified as either supervised or unsupervised, and further partitioned if the amount of works that fall under a certain scheme is significant. Moreover, different datasets and challenges found in literature and websites, containing masks of the aforementioned tissues, are thoroughly discussed, highlighting the organizers' original contributions, and those of other researchers. Also, the metrics that are used excessively in literature are mentioned in our review stressing their relevancy to the task at hand. Finally, critical challenges and future directions are emphasized for innovative researchers to tackle, exposing gaps that need addressing such as the scarcity of many studies on the vessels' segmentation challenge, and why their absence needs to be dealt with in an accelerated manner.