Hello fellows,
 In classic incandescent lamp, you could just "slice" the sinusoidal wave with the help of a potentiometer, diac and capacitor - or a MCU with zero-crossing circuit. EASY.

However, today we have dimmable LEDs bulbs. I'm considering make an alarm clock with AC output and a LED dimmable bulb, so it could wake-up with the light, simulating sun-rise. I'll 3D print everything... For sure, such devices already exists, however I wanna implement more features like temperature/humidity (because I can), bluetooth connection, proximity sensors, etc... So I'll make a custom PCB and firmware, and this will be my 30th birthday project.

The question is: Do you know which technique are applied to control/dim this kind of bulbs?

I'm electrician, so I already know the dangers of dealing with LIVE AC, how to mitigate and how to design Live AC safe pcbs with optocouplers --- don't worry about that.

thank you in advanced 

The easiest and cheapest way is to limit the current going to the LED with a potentiometer. There are programmable potentiometers available with current ratings suitable for some LEDs, if you want to use say a Raspberry Pi or Arduino.

The most efficient way is PWM dimming, where the led is switched on and off really fast, but the length of time it's on is changed. A little more complex, but still manageable for a DIY project.

You are not very clear on what you wish to do - to dim an off the shelf LED lightbulb or just an arbitrary LED?

Off the shelf lamp, assuming it is designated as dimmable, will respond to classic wave chopping phase dimming, usually both leading or trailing edge modes. You can DIY a dimmer circuit, or get an inexpensive module which takes some easy control signal like isolated 1-10V and does the dimming.

As for a bare LED, light output is about proportional to input current, which you can regulate in some way. Both analog and PWM will do.

You can play with DC led strips with some dimmer module, too, multiple of variants, PWM, WS2812, 10V, DMX, even Modbus.

AFAIK a trailing edge dimmer is better for driving dimmable mains powered LED lamps than leading edge. However, both will work.
The leading edge will cause a larger inrush current than leaving the leading edge as is and cutting off the trailing edge. So getting the trailing edge one, will put less heat into your lamp's rectifier and smoothing cap.

More info: https://sound-au.com/lamps/dimmers.html

For dimming the bare LED chips (so when you are designing the driver, so not the off-the-shelf mains bulbs):
Dimming with variable DC current may be easier, it can lead to uneven light output at low current settings.
Reasons differ whether we are talking about parallel or series connected LEDs.
With predominantely parallel configuration (e.g. the 12V LED strips) the variation of forward voltages cause the lower voltage ones to take more current than others, so shining brighter. The differences may come fro  both variation between individual chips, as well as temperature variations over the whole installation.
The problem with series chains is, as they age, LEDs tend to develop a parasitic current leakage path parallel to the structure. This parasitic current may reach few percent of the current they are mostly (from the wear perspective, so practically the highest settings normally used) operated at, stealing current from the light generating junction. With fixed current not that big deal (the few percent brightness difference is negligible), but once you reduce the drive current to similar few percents in an attempt to dim them, this leakage may steal all this current so the affected LEDs become way dimmer than the unaffected ones. And because this is related to defects in the crystakls and so completely random, each individual LED will have this parasitic current significantly different. So at a given light output (10% is only moderate dim level, normally it goes down to 1% or even below) thevariation across all the dies becomes quite ugly.

Therefore (plus the simplicity even when high efficiency is required) the PWM dimming is the favorite method in most lighting systems. Some may usecombination (current reduction down to a level where the unevenness is not yet a problem, so like 20..30%) and then below that go with the PWM.

If your problem is to make the clock display dimmable, it depends what is driving it.
When it is a microcontroller where you write the firmware, I would go for a PWM (vary the pulse width when the digit is on - use one timer overflow interrupt to trigger the digit turn ON, then the "compare" interrupt to turn thit off, vary the "compare" threshold to control the brightness).
Works pretty well even when used to compensate for battery voltage variation (constant brightness over 2..5.5V supply, no voltage regulator) or the number of segments lit when using just a single resistor per common digit terminal (so a 4-digit display needed just 4 resistors)
When dealing with a given clock chip (like LM8560 or so) where the timing is given, then varying the ballasting resistors (e.g. replacing them with transistor current sources) is, according to me, the easiest way to go (I used this to make the display brightness controlled by ambient light).