The general trend towards lightweight components and stronger but difficult to machine materials leads to a higher probability of vibrations in machining systems. Amongst them, chatter vibrations are an old enemy for machinists with the most dramatic cases resulting in machine-tool failure, accelerated tool wear and tool breakage or part rejection due to unacceptable surface finish. To avoid vibrations, process designers tend to command conservative parameters limiting productivity. Among the different machining processes, turning is responsible of a great amount of the chip volume removed worldwide. This paper reports some of the main efforts from the scientific literature to predict stability and to avoid chatter with special emphasis on turning systems. There are different techniques and approaches to reduce and to avoid chatter effects. The objective of the paper is to summarize the current state of research in this hot topic, particularly (1) the mechanistic, analytical, and numerical methods for stability prediction in turning; (2) the available techniques for chatter detection and control; (3) the main active and passive techniques.Thanks are addressed to Basque country university excellence group IT1337-19. The authors wish to acknowledge also the financial support received from HAZITEK program, from the Department of Economic Development and Infrastructures of the Basque Government and from FEDER funds. This research was funded by Tecnologico de Monterrey through the Research Group of Nanotechnology for Devices Design, and by the Consejo Nacional de Ciencia y Tecnologia (CONACYT), Project Numbers 242269, 255837, 296176, and the National Lab in Additive Manufacturing, 3D Digitizing and Computed Tomography (MADiT) LN299129
