Gas tankless water heaters are commonplace around the planet. In some countries the majority of homes use such systems as their only source of hot water. In other words they are reliable performers that are technologically well developed.
The tankless waterheaters that use gas achieve almost instant heating in a simple way. They spread the water out and apply flames - you can see a barrage of flames whoosh into life in the unit when someone opens a hot water tap. By spreading the water and making it thin it is possible to heat it at the speed it flows through the unit (measured in gallons per minute). Generally speaking, the bigger units do more spreading and apply more flames! This part of the unit is called a heat exchanger.
In slightly old fashioned on demand hot water heaters from five or ten years ago this was pretty much the model. It was not all that efficient however - plenty of the heat went past the water and was wasted, being expelled as hot air through the vents. As much as forty percent of the heat could be lost this way, and the manufacturers only got away with it because gas is fundamentally cheap compared with say electricity.
This is helpful to know, because modern tankless hot water heaters make use of this previously wasted energy. They use a condenser unit to use this energy and achieve efficiencies of ninety and above. These are the units you should look for.