What are the most important substances added to the refined base oils and
what do they do?

In the Dark Ages cars and bikes used blends of refined mineral oils 'straight' with nothing added. The trouble was, even in the slow-revving engines of 80 years ago the oil didn't last very long, and the engines didn't either. Black sludge and corrosion were the killers, and both were tackled in the 1950s with detergent and antioxidant chemicals. The detergents washed the carbon from fuel combustion off the bores and out of the ring grooves, and at the same time reduced bore and piston ring corrosion. The antioxidants stopped the oil reacting with oxygen in the air, which cut acid sludge formation which in turn reduced corrosion and oilway blockages.

Some antioxidants had the useful side-effect of reducing wear as well. This added up to longer oil and engine life, both improving about three times. (Straight oil had to be
changed every 1000miles, and even lightly-stressed engines running on it were ready for a full overhaul at 15-20,000.)

Later came dispersant compounds which held the carbon as tiny particles in the oil which didn't settle out anywhere, and slipped through the oil filter as if it wasn't there.(Solid bits in well-used modern oil are about 1/1000mm across; the pores in an oil filter are at least 15 times bigger.)

The other big problem with oil used to be cold starting. It was usual to have SAE 20 Winter or 'W' grades, and SAE 30 or 40 Summer grades, and even the so-called Winter types would defeat the starter in serious cold weather. Unfortunately, oil is very thick when it's cold, and very thin when it's hot. To have an oil thick enough to look after a hard working engine, you had to use a grade which was too thick when it was cold. The answer was (and is) multigrade! What was needed was an oil that behaved like a 20 'W' grade in the cold, but only thinned down to a SAE 40 or 50 when really hot; yes, 20W/50! This can be done by mixing thin oil with thick polymers based on plastics and synthetic rubbers; these don't do much in the cold, but as the oil warms up they unwind and
thicken it up to some extent. The oil still thins down, but not as quickly as a polymer-free or monograde type. Multigrades started to catch on around 1960, but these pioneer types were easily ruined by mechanical shear effects, more so in gearboxes than engines. These days the better quality polymers resist shear even in combined engine/transmissions, so it is essential to use good quality shear-resistant types in a performance car or motorcycle, which gives its oil a hard time in both engine and gearbox.