The static stability of hexapods motivates their design for tasks in which stable locomotion is required, such as navigation across complex environments. This task is of high interest due to the possibility of replacing human beings in exploration, surveillance and rescue missions. For this application, the control system must adapt the actuation of the limbs according to their surroundings to ensure that the hexapod does not tumble during locomotion. The most traditional approach considers their limbs as robotic manipulators and relies on mechanical models to actuate them. However, the increasing interest in model-free models for the control of these systems has led to the design of novel solutions. Through a systematic literature review, this paper intends to overview the trends in this field of research and determine in which stage the design of autonomous and adaptable controllers for hexapods is.The first author received funding through a doctoral scholarship from the Portuguese Foundation for Science and Technology (FCT) (Grant No. SFRH/BD/145818/2019), with funds from the Portuguese Ministry of Science, Technology and Higher Education and the European Social Fund through the Programa Operacional Regional Norte. This work has been supported by the FCT national funds, under the national support to R&D units grant, through the reference project UIDB/04436/2020 and UIDP/04436/2020
