Severe convective weather forecasting is one of the challenging tasks in forecasting operations, with the monitoring, forecasting and early warning of tornado being particularly difficult within this field. This paper briefly summarizes the history of tornado monitoring and forecasting operations in the United States, Europe and China, focusing on the advances in the monitoring, short-range and short-term forecasting and early warning technology of mesocyclone tornadoes. Tornadoes are of a small spatiotemporal scale, and short-range and short-term forecasting can only predict their favorable environmental conditions and mesoscale formation mechanisms, respectively. The significant tornado parameter (STP) and the maximum updraft helicity (UH) are the effective physical variables for short-range and short-term forecasting of tornadoes, respectively. The monitoring of mesocyclone tornadoes relies on the tornadic vortex signatures and polarimetric observations from dual-polarization Doppler weather radar, which can monitor the formation and dissipation of tornadoes. It is still difficult to directly identify the tornadoes produced by quasi-linear convective systems, but the relationship between mesovortices and tornadoes in such storms is relatively close, and technical methods have been developed to use vertical wind shear and radar dual-polarization characteristics to identify the development of mesovortices in such storms. The ability to identify and forecast tornadoes using physical laws, random forests, or deep learning methods has significantly improved, while there are still significant shortcomings in the monitoring, forecasting and early warning capabilities of tornadoes. In future, we need to improve monitoring and identification capabilities with more observing or detecting methods, deepen understanding of mechanisms, develop ultra-high resolution numerical weather prediction models and artificial intelligence methods to enhance forecasting and early warning capabilities. It is even more crucial to fully leverage the subjective initiative and pivotal role of forecasters.