How do LED light bulbs work?

There are several circuits on the internet from noatable sources that show how LEDs can be powered directly from an AC supply without a transformer. Here's one from ON semi: -

And here is the document it came from. The document is entitled "High Current LED - capacitive drop drive application note".

Here is another interesting article, this time from EDN. It shows the following diagram, again transformerless: -

And another article and circuit here: -

Depends on the led light bulb. Some are direct dc bulbs. These are meant for 12v lamps, not AC lamps. These are smaller, lack the ac rectifying parts, normally set up with 3 leds + resistor or small current controlled ic, in a ceramic casing.

Now LED bulbs that are meant to be replacements for standard 120v incandescent bulbs are very similar to CCFL bulbs. They have AC rectifying section, most are half wave. Then they step it down, then use a current control section to provide the final step for the lighting. If it is a Fading led bulb, there would be more circuitry inside for that.