In 5th edition, would detect magic reveal illusions such as invisibility, disguise self, etc. by the rules as written? While it would not reveal the nature of the illusion, it would reveal that one is present I believe.
I know some illusion spells refer to true seeing and see invisibility which are clear that they bypass illusions.
I just imagine this can be problematic as the warlock can cast detect magic at-will at third level.
By strict RAW, you can sense the presence of illusions of all kinds, but you can't actually see exactly where they are, or that they are illusions rather than just some kind of magic in your vicinity. From the description of Detect Magic:
For the duration, you sense the presence of magic within 30 feet of you.
Simple enough; if there's magic, you can sense it.
If you sense magic in this way, you can use your action to see a faint aura around any visible creature or object in the area that bears magic, and you learn its school of magic, if any.
If a creature or object is covered by an illusion, they're not a visible creature or object, and the illusion itself is neither a creature nor an object, so you can't see its aura. An illusion that is not being "borne" by a creature or object is likewise not a visible object or creature, so you can't see its aura, either.
Where things get messy is if there is a creature or object that "bears" an illusion but is still visible. However, I can't find any cases that would fall under this category. For example, you could use Minor Illusion to cover someone's head, but that is a freestanding illusion that happens to be around a creature, rather than actually being borne by that creature.
As far as whether you want Detect Magic to function by strict RAW in your game is concerned, given the way you've phrased this question I assume you're more worried about it being too powerful than the opposite, so this should suit you.
Yes. The detect magic spell allows you to "sense the presence of magic within 30 feet of you. If you sense magic in this way, you can use your action to see a faint aura around any visible creature or object in the area that bears magic, and you learn its school of magic, if any." (Source)
There is nothing to indicate that a spell of the illusion school would cover up this aura. Even with an invisibility spell, you become aware that there is an illusion aura in a certain space. You don't learn anything about the object on which the aura is placed (except general size perhaps) and what kind of spell it is, but having an illusion aura hover in mid space is a very strong hint that it most probably is an invisibility spell.
A person under the effect of an invisibility spell could still attempt to hide normally to avoid being within the sight of the spellcaster, but he would have to be behind cover that can block the aura. (1 foot of stone, 1 inch of common metal, a thin sheet of lead, or 3 feet of wood or dirt.)
