Extreme warm water events known as Marine Heatwaves (MHWs) exert adverse impacts on ecosystems and economies. Currently, definitions of MHW events are all based on temperature timeseries at a single location, which limits the characterization of their spatial structures. In this study, we extend the definition of MHW events from the time domain to the spatio-temporal framework. The proposed definition involves constructing snapshots of MHWs with a spatially compact structure and tracking their evolution with time. The tracking is semi-Lagrangian as it tracks the MHW events rather than the water mass. A set of MHW metrics are introduced to measure the spatio-temporal characteristics of MHW events. Applying the new definition to the observational sea surface temperature dataset during 1982-2020 yields 8642 MHW events after excluding those occupying an equivalent area smaller than 5 degrees x5 degrees or lasting for less than five days. Longer-lasting MHW events tend to be larger in spatial extent and vice versa, whereas the intensity of MHW events is nearly independent from the duration and spatial extent. MHW events typically exhibit a growing, mature and decaying phase in sequence during their life cycles. The spatial extent and intensity reach their primes around the center of the life cycle. Many of the MHW events exhibit evident displacement during their life cycles with the zonal movement stronger than the meridional movement. Eastward movement is dominant for MHW events in the mid-and high -latitude regions but the opposite is true in the tropical ocean. In response to the anthropogenic warming, MHW events have occurred more frequently and become longer, larger and stronger.