The objective of this paper is to give a review of the main works dealing with mathematical modeling of blood cell formation, disorders and treatments within the past fifty years. From the first models to the most recent ones, this research field has inspired many leading experts in mathematics, biology, physics, physiology and computer sciences. Each contribution was a step further to the understanding of these complex processes. This work summarizes the key ones and tries to show not only the evolution of the interest for this problem but also the different research trends throughout the decades up to the latest models of the past years.