Dimming a light source used to be very simple. The reason is that with the old incandescent bulbs, dimmers functioned much like a tap; if you turned down the tap, less water came out - i.e., if you adjusted the dimmer downwards, less light came out. Dimming an LED bulb is quite a different matter, as the dimmer must now be able to work together with the electronics found in all LED bulbs.
LED is very suitable for dimming, but you must be aware that not all dimmable LED bulbs will work with your current dimmer. This is due to modern LED bulbs not being adapted to "communicate" with older dimmers, as these are very different technologies. With some dimmable bulbs, you might be lucky and the old dimmer will be compatible with the bulb, but most often you will find that the two are not compatible - among other things, you might experience humming, noises, flickering etc. Therefore, buying an LED dimmer is always a good idea, as it is adapted for very low power consumption and the electronics of LED bulbs.
It is also worth noting that not all dimmable LED lamps can be dimmed down to the off state. Some bulbs will only be able to dim to 10-20% of full brightness. This may be due to the bulb not being designed for further dimming, or because the dimmer is not sufficiently loaded - the latter is discussed in the section below.