What are the types of headlights out there?

Most cars come with halogen headlights. These are the most common but newer and more expensive options exists like Xenon or HID and LED lights as well.

Halogen:

Halogen headlights use a tungsten-halogen filament mixed with halogen gas to generate a much brighter light than conventional headlights.

Xenon/HID:
Xenon is one type of HID (high intensity discharge) bulb. Instead of using a heated filament, Xenon headlights use gas. Xenon lights are brighter, have a lower operating temperature, and last longer. Also keep in mind that HID bulbs can be a bit pricier and professional installation may be recommended.
LED:
LEDs (light emitting diodes) have an advantage over halogen in that they draw less power to operate, run cooler than halogen lights, and last longer. If your newer vehicle came equipped with LED headlights from the factory, you’re probably not even reading this article.