Why didn't we see many VTOL aircraft in the history of aircraft development?
VTOL (and STOVL) are concepts which were conceived as a result of not having large aircraft carriers or the space for a long runway. The primary feature of these aircraft is to enable them to take off and land using a minimum of runway distance, but in order to achieve this compromises have been made with the designs. This affects several aspects of the aircraft; complexity goes up as it requires at minimum additional controls for low-speed maneuvers where traditional control surfaces are inefficient and some way to distribute the thrust or add thrust to balance when flying vertically. 

This tends to add weight and occupy internal volume which could otherwise be used for other things, such as fuel. It drives complexity when flying the aircraft and also in terms of maintenance, and thus cost. 

Take the F-35 as an example. There are three models of a single design, where the A-model is designed to operate from regular air bases on land, the B-model for VTOL operations on amphibious attack ships or forward air bases, and the C-model for regular aircraft carriers. Compared to the other two models, the B-model has less internal fuel and a lower max takeoff weight. Because of this it will be required to refuel more often and/or carry less payload, which in turn will drive the complexity of operating the aircraft due to the logistics. 

Another issue with VTOL airplanes, is that they (as far as I can tell) haven't been designed to takeoff vertically with a full fuel load and carrying a full payload. I could not find any numbers for the F-35, but for the AV-8B+ Harrier the max vertical take-off weight is around 9,5 tons, while a rolling take-off increases this to 14 tons. ([Wikipedia])1 This is quite a difference, and it shows how much you sacrifice to be able to do a vertical takeoff. 

While having the option of VTOL is nice, cost is generally what drives decisions (even in the military). An AV-8 cost around \$19.000 USD to operate per hour, according to DefenceIssues. While older than eg. a JAS-39 Gripen (age tends to drive costs upwards), the Gripen which is of a similar size and empty weight has a longer range and only cost $4.700 USD per hour to operate. And according to the source that number is high, as labor costs more in Europe than in the US. 

Use on aircraft carriers

While some VTOL aircraft have been developed, the reason for why they aren't used more is related to everything above. Many of the non-VTOL carrier aircraft used today have a basis in aircraft originally designed to operate from land-bases using regular runways. If you decide to use VTOL aircraft on an aircraft carrier, the carrier can generally be smaller than a carrier operating STOL or catapult-launched aircraft, but this will also affect how you can use the carrier.