This chapter reviews the current state of knowledge about global chondrichthyes bycatch, including how the combination of biological characteristics of these species and the impact of different fishing methods reflect their vulnerability to bycatch. Specifically, it summarizes the present status of elasmobranchs and chimaeras bycatch worldwide. Following this, it illustrates the main ecological consequences behind such incidental captures. Hence, it provides a description of how chondrichthyes bycatch occurs across broad fishing gear categories. Moreover, it outlines potential mitigation options available to reduce bycatch. As such, the main technical measures tested and applied in different fishing practices are listed. In addition, an overview about which are the current management measures implemented at international level to ensure long-term conservation of cartilaginous fish is reported. Then, two case studies summarize how chondrichthyes bycatch occurred in some of the most exploited fishing areas. Finally, the chapter ends with relevant considerations about potential for new research needed to monitor and reduce chondrichthyes bycatch.