There are two feature of Babylon.js that handle events, actions and observables. It is also possible to use plain Javascript.
Observables are the latest addition to Babylon.js and their aim is to make event handling within Babylon.js more consistent and coherent for developers of Babylon.js.
Playground Example of Observables -
Using actions events are managed with the actionManager along with triggers such as onPickTrigger to determine if a mesh is clicked or touched and onKeyDown to determine if a key is pressed during a scene.
Playground Example Move Sphere with actionManager and Key Presses -