Is it true that you can't smell anything when you're asleep, or is this a myth?

Actually it depends on what stage of sleep you are in, but in general, your olfactory system can still register certain smells, but not as effectively as when you are awake.

When you first fall asleep your sense of smell shouldn’t change drastically, but becomes gradually less sensitive, the deeper you go. It will probably take a stronger smell to elicit a response.

During the next stage, known as Slow Wave, the olfactory receptors become further diminished, to the point that you would be unlikely to react to external smells.

The more complicated stage is during REM Sleep, when we tend to dream, the olfactory receptors seem to work in a less consistent pattern, external smells are not usually registered but the brain can generate its own olfactory sensations - so you may think that you have smelt even quite strong scents, but it is imagined, without an actual external stimuli.

However, it doesn't seem that the olfactory sense is entirely switched off during sleep, as the brain remains capable of detecting some odours and will still generate olfactory experiences. As with so many things, individuals can differ markedly in how sensitive their olfactory sensitivity is when sleeping. Medication, alcohol and sleep disturbance can all have an influence. There are certain sleep states or disorders in which people can experience unusual smells, or olfactory hallucinations. These experiences are rarely reported and it is likely they are associated with specific medical conditions.

So, it would be better not to rely on your sense of smell whilst sleeping, but some activity is still present as you are drifting off.