Run orders in factorial designs have been a topic of interest in recent decades because the basic principle of randomization does not necessarily eliminate the bias caused by unknown factors and also generates many level changes, making experimentation more expensive. Therefore, the literature in this area has addressed the construction of preestablished run orders to eliminate the bias produced by unknown factors and/or minimize the cost of the experiment. This paper presents the results of a systematic literature review (SLR) and a taxonomical classification of studies about run orders for factorial designs published between 1952 and 2021. The objective here is to describe the findings and main and future research directions in this field. The main components considered in each study and the methodologies they used to obtain run sequences are also highlighted, allowing professionals to select an appropriate ordering for their problem. This review shows that obtaining orderings with good properties for an experimental design with any number of factors and levels is still an unresolved issue.