The biggest change is that the drag reduction system (DRS) -- a moveable flap on the rear wing that flips open to increase straight-line speed -- can now only be used in designated zones at each circuit.
Many teams, and in particular Red Bull, had used it freely in practice and qualifying to increase their lap times. They won't be able to do that this year.
Teams can also no longer use DRS to affect other aspects of car performance -- a trick pioneered by Mercedes in 2012.
Flexible front wings had also been used by some teams -- Red Bull were usually under scrutiny -- to increase the aerodynamic flow of the car. However, a new ruling says front wings can now only bend by 10 millimeters, and tougher load tests will make sure teams are sticking to the rules.
What they can do, however, is add a "vanity panel" to the top of their car to hide the unsightly stepped noses.
8. Burning rubber
Tires are once again the biggest unknown for the teams heading into 2013.
Pirelli's new rubber is softer and the tire structure is more flexible with reinforced shoulders. A set of 2013 tires adds an extra 2 kilograms in weight, so the minimum weight for each car has increased to 642 kg.
Lap times on the 2013 tires are expected to increase by around half a second a lap. At the Barcelona circuit, which hosts the Spanish Grand Prix, many cars set lap times in testing this month that were quicker than pole position for the 2012 race.
Pirelli also wants to make sure teams need to pit at least twice during the race.
Tire degradation was mixed during testing but the colder temperatures in Spain mean performance there is not an exact benchmark for the warmer climes coming up in the first two races in Australia and Malaysia.
Pirelli effectively pays to supply tires to the F1 grid in a negotiated deal which also include track-side advertising. The teams also pay it a small contribution, but the bulk of the bill for the season's 36,000 spheres of rubber is picked up by the tire supplier.
The Italian company is now entering the final season of its three-year contract as F1's official tire supplier. Pirelli says it is intends to carry on -- but only if the financial conditions are right. A decision may be made in the first quarter of 2013.
9. One eye on 2014
While uncertainty exists about the tire supplier's future involvement, major rule changes for 2014 present a financial and technical headache for F1's teams.
Next season they must use six-cylinder turbo engines with a greater share of power gathered from kinetic energy recovery systems.
But with change comes opportunity, and that is why many teams -- especially those who don't expect to be at the sharp end of the championship -- have already shifted a large share of their resources to the development of next year's car.
Until then, the mighty V8 engines look set to power a battle royale when the 2013 season roars into life in Australia this weekend.