LEDs are current driven devices
Electronic

A LED is described as a CURRENT DRIVEN DEVICE.

This means the illumination is determined by the amount of current flowing through it.

This is the way to see what we mean:

Place a LED and 100R resistor in series and connect it to a variable power supply.

As the voltage is increased from 0v, to 1v, the LED will not produce any illumination,

As the voltage from the power-supply increases past 1v, the LED will start to produce illumination at about 1.6v to 1.7v (for a red LED).

As the voltage is increased further, the illumination increases but the voltage across the LED does not increase.
(It may increase 0.1v) but the brightness will increase enormously.

That's why we say the LED is a CURRENT DRIVEN DEVICE.

The brightness of a LED can be altered by increasing or decreasing the current. The effect will not be linear and it is best to experiment to determine the best current-flow for the amount of illumination you want.

High-bright LEDs and super-bright LEDs will illuminate at 1mA or less, so the quality of a LED has a lot to do with the brightness. The life of many LEDs is determined at 17mA.

This seems to be the best value for many types of LEDs.

1mA to 5mA LEDs

Some LEDs will produce illumination at 1mA. These are "high Quality" or "High Brightness" LEDs and the only way to check this feature is to test them @1mA as shown below.

THE 5v LED

Some suppliers and some websites talk about a 5v white or blue LED. Some LEDs have a small internal resistor and can be placed on a 5v supply. This is very rare. Some websites suggest placing a white LED on a 5v supply.

These LEDs have a characteristic voltage-drop of 3.6v and should not be placed directly on a voltage above 3.6v. If placed on a voltage below 3.6v, the LED will not glow very brightly.

If you have a voltage EXACTLY 3.6v, you can connect the LED, but most voltages are higher than 3.6v and thus you need a resistor.

The only LED with an internal resistor is a FLASHING LED. These LEDs can be placed on a supply from 3.5v to 12v and flash at approx 2Hz.

The LED is very weak on 3.5v but it flashing can be used to drive a powerful LED (see circuits section). It can also be used to produce a beep for a beeper FM transmitter.

NEVER assume a LED has an internal resistor. Always add a series resistor.

Some high intensity LEDs are designed for 12v operation. These LEDs have a complete internal circuit to deliver the correct current to the LED.