Today, it's generally solved by having an airtight sheet (plastic) between the insulation and the inner wall. Sometimes placed inside the insulation. This ensures a temperature gradient that will not cause condensation inside the house.

You'll generally put a sheet that's porous but not airtight outside the insulation, to reduce heat loss due to convection and also provide an extra layer of defense against moisture damage due to wind-blown rain.

This technique necessitates good ventilation (often powered) if it's used throughout the entire house. This is to avoid saturating the inside air with humidity due to breathing and other activity, itself leading to the condensation you're trying to avoid. It can sometimes be just on e.g. floors and ceilings. Then, the rest of the structure might still be leaky enough that mostly passive ventilation will do the trick.

Older houses handle the problem by just being so leaky that condensation won't be a problem.