There are two forms of forced induction, and one of them seems to have vaporized over the years. Why is that the case?
In the world of engines, you can get them in either petrol or diesel flavours. But whichever you pick, you can go even further with the choice of either natural aspiration or forced induction. As a quick recap, natural aspiration means that the engine sucks in air which it uses to burn fuel entirely by itself (the engine generates a vacuum as it spins), while forced induction means you're cramming air down the throat of the engine.
Naturally, the latter lets the engine make more power. It's simple: more air in the engine means you can burn more fuel, and more fuel means more power. Over the decades of internal combustion, there have only been two ways to achieve this. What we're seeing more and more nowadays is turbocharging - especially with downsized, smaller capacity engines. This form of forced induction uses waste gasses from the exhaust to spin a turbine that in turn forces fresh air into the engine.
The other form of forced induction has become a fair bit rarer, and it's what is known as supercharging. Superchargers don't use exhaust gasses to spin up, but rather directly connects to the spinning crankshaft of the engine. There are different kinds of superchargers, but they all operate on that same principle. One of the main advantages of a supercharger is instant response since the supercharger is always spinning and forcing air into the engine - but there are a couple of downsides too.
Superchargers are tricky things to package because they take up space in the engine bay, and they add complexity to the belts that drive various other accessories in the engine. More than that, by nature of design they also add parasitic losses to the engine as it takes energy to spin the supercharger. Granted, the supercharger helps the engine to make more power as it spins, but it also takes back a certain percentage to operate.
The other issue with superchargers is that they generate an immense amount of heat, more so than what turbochargers generate. Different types of superchargers are differently susceptible to this, but generally supercharging increases the temperature of the air that goes into the engine and that can be extremely bad for performance. But are these the only reasons that manufacturers have decided to stop supercharging their engines?
In the early era of turbocharging, they tended to be fairly large and inefficient. They provided extra air, but they took a lot of time to deliver that air. This delay, known as turbo lag, was one of the reasons that made turbocharging a lot less appealing for mass-market applications. Eventually, turbocharger manufacturers got wise and made smaller, quicker responding turbos that have almost no lag - basically giving you that massive amount of torque even at low engine speeds.
There was once a time when superchargers were fairly common - Mercedes-Benz had their Kompressor models, Toyota had their GZE engine variants, and Audi made use of the supercharger for their V6 engines. Nowadays, the number of models packing superchargers from factory are significantly lower. The Dodge Hellcat and Demon models still fly that supercharger flag high, while Lotus still uses them for a number of their models and Toyota last implemented a supercharger with their previous-generation Yaris GRMN.
The reasoning for this is that the near-instant response of the supercharger took priority over every other drawback. For Dodge's models, the supercharger provides massive amounts of torque that helps to get their cars down the drag strip in no time. With mid-engine cars like the Lotus Exige, Elise, and Evora, even small amounts of turbo lag can ruin driveability and precision. And with the Yaris GRMN, well Toyota just decided they wanted to make their hot hatch easier to drive.
But outside of those specific applications, there really isn't a reason for a supercharger to be a part of the equation. A turbocharger produces more power, does so more efficiently, and is more easily packaged with the engine to make for a total win in all situations. They turn small engines into giant killers, and big engines into world-beaters. For all of that, there is still the novelty of a supercharged engine - whether it's the whine as it spins or the razor-sharp response.