This article is a corrected and extended version of the invited paper that appeared in the proceedings of Automata'13, 19th International Workshop on Cellular Automata and Discrete Complex Systems, LNCS 8155, 2013, p. 15-30, doi:10.1007/978-3-642-40867-0 2 Research on asynchronous cellular automata has received a great amount of attention these last years and has turned to a thriving field. We survey the recent research that has been carried out on this topic and present a wide state of the art where computing and modelling issues are both represented.