There are two things here - inverted systems, and engines mounted inverted.
To take the latter first, an example is the Gipsy Major fitted to the Chipmunk and Tiger Moth. It's an in-line 4, and if it was mounted 'right way up' with the crankshaft output to the prop on the correct thrust line, the cylinders would stick up in front of the cockpit and limit the pilot's view ahead. Some early Moths and other aeroplanes are like this.
To obviate this, the engine is fitted with the cylinders hanging down, beneath the crankshaft. This allows the thrust line to be up high, without the cylinders getting in the way of the view forward. This is an 'inverted engine' installation (the carburettor is, of course, mounted right way up). Apart from being aware of the possibility of oil draining into the cyclinders while the engine is off, is of no real concern to the pilot.
Inverted systems, however, refer to the ability of an engine to continue to develop power regardless of whether the aeroplane it is fitted to is right way up or upside down. To acheive this it will need either fuel injection or a special carberettor (normal carbs - like that fitted to the Chipmink - will cease to function when inverted). It will also need some means of ensuring that the oil system continues to operate, so that the engine will not be damaged through oil starvation while dveloping power when upside down.
SSD