- Advances in rocket engine design & tech to enable deep throttling
- Control algorithms for propulsive landing maturing (Google "Lars Blackmore", "GFOLD", "Mars Landing", and work through the references)
- Forward thinking and risk-taking by SpaceX to further develop tech demonstrated by earlier efforts (DC-X, Mars Landing, etc.)
Modern simulation and sensor capabilities helped, but were not the major enabling factors.
So they need to "hoverslam", that is, arrive at the landing pad rapidly decelerating so that their altitude hits zero just as their speed hits zero. This was thought to be very hard, but I don't think SpaceX has lost a stage due to estimation failure there. It helps that there is significant throttle range and fairly rapid throttle response on the engines, so they can have some slack. (Plan to decelerate at 2.5g for the last ~20s or so, with the ability to do anything between ~1.5g to 4g, so you can adjust throttle based on measured landing speed.)
Their Superheavy has more engines, allowing them to bring the TWR below 1, enabling hovering.