Over the years, I have installed many tankless water heaters (or on demand water heaters) in customer homes, including my own.
Manufacturers have made tankless water heating an attractive way
to deliver a continuous supply of hot water anywhere in your
home. Efficient, convenient and affordable, these units can deliver more than satisfactory energy savings, and use much less space as conventional water heaters.
The unit heats water only when a faucet is turned on or flow is sensed through the unit. They use energy sources such as propane, natural gas, or electricity to effectively heat water as it passes through the heat exchanger. When the water flow stops, the unit flow switch or sensor turns the unit off, using no energy or fuel while sitting off. Thus, holding and heating no water in a storage tank. 
Tankless water heaters are becoming a standard installation in new construction and a desirable upgrade to older homes. The installation in a new home is quite simple while venting the unit out of an old foundation can be a challenge. I’ve found that the units can be installed in a number of configurations due to it’s compact size. Installation can be simple in camps, homes, mobile homes, outside locations (in warmer climates or camps), closets, or just about anywhere you can fit the units that have adequate access to service them. Most of the time it would be installed on an outside wall and vented directly to the outdoors. In some rare instances, I’ve had to do some extensive exhaust piping that could end up very costly to the homeowner.
In commercial applications, tankless water heating has it’s advantages as well. Units can be cascaded together to deliver hot water to multiple plumbing fixtures at the same time. You will find them at restaurants, hotels, motels, schools, public facilities, industrial facilities, nursing homes, and many more applications.
A tankless water heater is somewhat of a costly investment up front, but may provide substantial savings. A conventional water heater stores hot water and as the water is used or is lost through the tank walls, will operate over and over to maintain water temperature. This creates a continuous operation cost, while tankless water heaters run only when water passes through it.
If “instant” hot water is desired, a recirculation loop with an aquastat to control loop temperature may be installed to the plumbing system. This is frequently found in long water line runs and in commercial applications such as hotels where hot water is needed at the faucet as soon as it is turned on while the supply water may be hundreds of feet away.
There are some disadvantages to tankless water heaters. The initial purchase price is approximately double or even triple, depending on individual installation circumstances, the wait for hot water at the tap is usually delayed slightly due to the unit having to start heating water as it passes through, and is depends on proper flow to operate. In hard water applications, there have been known issues with build up in the heat exchangers and filters causing the unit to stop working. In this case it may be necessary to soften and filter the water before entering a tankless heater.
Despite some inconveniences, the tankless water heating system has proven to be a better alternative to conventional tanked water heaters, making it a great choice for water heating in most applications.