Note that this info is for fairly low power LEDs. When you start having high power LEDs, regulations may require better power electronics, and the cost of the electronics might be amortized against the cost of the thermal cooling solution, etc, so you can make a more expensive electronics package.
1) By stringing ~ 180v of LEDs in series, and adding a current limiting resistor, you can drive the whole thing from the AC line. This has terrible variability (short light spikes every 60hz, and the thermal effects will change the LED properties so much that you could easily have 2x light intensity change as they warm up) and poor total illumination (as most of the cycle is spent with the AC waveform lower than the needed voltage. I haven't seen this in the wild, as option 2 isn't much more expensive and far better.
2) Use a single diode + capacitor rectifier to generate ~180v, and then have a similar string as in (1). This gives far better illumination (the capacitor will probably stay in the 160-180v range), but still has substantial 50/60hz ripple based on the size of the capacitor
3) Similar to (2) but use a full bridge rectifier instead of a single diode. As we are now driven by a rectified sine wave, the ripple voltage will ~half, and the ripple frequency will now be 100/120hz.
4) Many applications don't have ~60 LEDs in series, so you can't drive directly from the rectified AC line. The first stage is a rectifier, and a second stage most likely is a buck converter. The quality of the light out of this depends on how much you care about power factor. Chips like NCL30288, for example, maintain high power factor and fairly low lighting ripple. Most people won't notice this.
5) Particularly in higher power lighting, a separate power factor correcting stage achieves high power factor, and a second stage generates a constant current that should have exceptionally low luminous intensity ripple (if designed right). The ripple frequency should be in the hundreds of kHz as well, so I don't think any eye could notice this.
And don't get started on dimming, I haven't found a product on the market that does non-phase cut dimming in <20W lights.