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What happens with a spell when it is cast in a smaller space/area than the actual spell itself? Does it simply not work? Does it adapt to the size of the room etc?
For example: Ice Storm casts at a 20ft radius and 40ft high cylinder. If it is cast in a 30ft room but the ceiling is only 20ft high, what happens?
The answer is implicit in the section of the spellcasting rules on areas of effect (Player's Handbook, Chapter 10):
A spell's effect expands in straight lines from the point of origin. If no unblocked straight line extends from the point of origin to a location within the area of effect, that location isn't included in the spell's area. To block one of these imaginary lines, an obstruction must provide total cover, as explained in chapter 9.
Obstructions that provide total cover, such as dungeon walls or floors, therefore limit the area of effect. This would mean that in your example, the cylinder goes from floor to ceiling, but not above, as the ceiling provides total cover to anything above it excluding the presence of holes.
As Anaximander's comment (below) puts it, you can think of the Area of Effect as light originating from the point of origin. If a target inside the Area is fully shadowed, it has total cover and is not affected, unless the effect is stated to spread across corners.
Area of effect spells radiate from the user and are blocked by walls, floors, and other bits of scenery.
From a mechanical standpoint, it ends there. One must also take into story telling, though.
How does the scenery react to the the spell? If a fireball (a 20x20ft area of effect) explodes in a small, 10x10ft cabin, are those walls staying in tact? Is the roof?
A spell will never pass through scenery, but it can shift and manipulate scenery in such a way that the area of effect expands beyond its initial bounds.
