To (hopefully) clarify, LEDs are in fact intrinsically "dimmable". Their light output is conventionally dimmed by holding voltage more-or-less constant and reducing current.
But incandescent lamps are typically dimmed by reducing average voltage, not current. So in practice, standard, conventional TRIAC-based dimmers are not well suited for dimming LEDs because they dim by reducing average voltage and current is held more-or-less constant (varies with filament temperature) during conduction.
Another issue is the 'dimmer curve' of particular wall-mounted dimmer. One description of a dimmer curve is the relationship between the rotation (in degrees) of a physical dimmer knob to the phase angle (in degrees)of the TRIAC conduction (output). A typical household dimmer curve that is appropriate for incandescent lamps may not be appropriate for an LED-based lamp. This issue is well addressed by emerging electronic solutions as well as by some existing conventional 'professional' dimmer consoles and panels such as those used in entertainment venues using DMX (DMX512)
There is at least one IC on the market that addresses both the current-control and dimmer-curve issues by interpreting the complex "chopped" waveform created by a TRIAC-based dimmer into the information needed by an LED for continuous dimming with a useful dimmer curve and then providing the appropriate current to the LEDs.
National's LM3445 detects the 0-180 degree phase angle of a conventional TRIAC dimmer output and translates that information into a current output with a 1:100 dimming range (about 6-1/2 f-stops of light).
HTH ... Marc Marc_F_Hult