Is engine timing even a thing anymore or does the computer handle everything now?
The short answer-yes the computer handles everything.
The longer answer-back in the days before electronics as we know them even existed, a man named Charles Kettering devised an ignition system that was in common use from the teens to the 70s.
The Kettering system has at its core a set of breaker points, a wire-wound coil, and a condenser. When the points are closed, current flows through the primary(low voltage or low tension) side of the ignition coil until it is saturated. When the points open, the current in the coil collapses, and the resultant collapse generates a high voltage(high tension) discharge on its secondary side. This voltage is funneled to a spark plug, which has a small gap. A spark jumps the gap, and hopefully ignites the air/fuel mixture in the cylinder.
Proper running of an engine(any gasoline engine) is dependent on the spark happening at the correct time in the rotation of the crank shaft. Ideally, the air/fuel mixture will be completely ignited, and cylinder pressures at their highest, when the piston reaches top dead center(TDC) on the compression stroke. To ensure this happens, the spark must be initiated some time before the piston reaches this point. The spark
timing is measured in crankshaft degrees before top dead center(BTDC). The proper timing depends essentially on two variables-the engine rotational speed and the engine load. Also, for the sake of both maximum power and efficiency, it is desirable to advance the spark(make it fire earlier) as much as possible without causing detonation, which is a sudden burn of all the air/fuel mix in the cylinder, and can cause both power loss and engine damage. In general, low load and high rotational speed-i.e. constant speed cruising-call for more spark advance(advanced timing) where high load and low rotational speed(acceleration from a stop) call for less advanced(retarded) timing.
In early cars, the ignition timing was accomplished by a relatively simple mechanical computer called a distributor, which is generally driven directly off the camshaft(in a 4 cycle engine, the camshaft runs at 1/2 the crank speed). The distributor accomplishes a couple of things. The first and most visible part is taking the high tension discharge from the coil and "distributing" it to the correct cylinder. This is accomplished in the "top" part of the distributor using the distributor cap, a rotor fitted to the center shaft, and of course the spark plug wires. Essentially, the coil discharge is fed into the center of the distributor cap and through a carbon button that contacts the rotor. The rotor "points" to the terminal for the cylinder which needs to be fired, and the spark will travel to that cylinder.
The second function of the distributor is buried a bit further down and consists of two parts-a cam on the distributor shaft with lobes corresponding to the number of cylinders, and the breaker points("points") mentioned above that ride on this cam. The cam serves to open and close the points. In this portion, there is one important variable-the amount of time that the points allow the coil to charge, called the dwell. This is measured in degrees. It is adjusted by changing the fully-open gap on the points(on an MG, you shoot for around 15 thousandths of an inch).
The third function of the distributor is buried even further down, and controls exactly when in the rotation of the engine the spark will fire. This is called the advance mechanism. It usually consists of two parts. The primary one is called centrifugal advance, and essentially advances the timing as the engine spins faster. The second is called vacuum advance. Engine load can be indirectly measured by monitoring the intake manifold vacuum. Low load results in high vacuum, and high load in low vacuum. The vacuum advance unit on the distributor translates a vacuum reading into a specific amount of spark advance. The amount of centrifugal advance is determined by the weight of the advance weights and strength of the springs, while vacuum advance is generally changed by changing an external vacuum "can". As an example-and I'm citing MGBs because I know these numbers off the top of my head-the desireable earliest distributor would add 0º of centrifugal advance over the base timing(more on that in a second) at idle, and 12º at 3000rpms. The vacuum advance can would be marked 5-15-5, which indicates that vacuum advance starts at 5"Hg vacuum, is fully on at 15"Hg Vacuum, and adds 5º advance maximum.
The variable most often adjusted when talking about timing is the "base timing", which basically sets the starting point of the distributor advance curve. This can be done in two common ways-statically and dynamically. For static timing, you rotate the engine to the specified base timing position(there are marks on the harmonic balancer to show this), then physically rotate the distributor body so as to just "catch" the points closing. The preferred way is to set it dynamically, which is done by using a timing light, as shown above. The timing light is generally clamped onto the #1 cylinder spark plug lead, the engine started, and the light pointed at the timing indicators. A xenon lamp in the timing light flashes every time the engine sparks, "freezing" the timing mark. On MGs, I generally skip the idle advance setting, and instead set to 32º maximum advance(vacuum disconnected) which is an optimum value for most cars(although I run mine at 34º on premium gas).
All of the above worked well for 60 years, but it has some issues. One of the most troublesome spots is in the breaker points, which are a wear item. When a new set is installed, they generally need to be readjusted after a few hundred miles as they bed to the cam. They also generally last for 10,000-15,000 miles. They can carbon up and have other issues that will leave you stranded(I carry a points file and a spare set of points in the MG). Also, they are prone to misfire at all speeds, but especially at higher speeds, something which is bad both for power and emissions.
In the 1970s, solid state electronics became practical, and one of the first things to do was replace the points with an electronic "ignition amplifier." This would read the cam directly(usually either optically or magnetically) and electronically modulate the voltage to the coil. This removed a maintenance item from the distributor, and had a bunch of other benefits. These systems can often be retrofitted to cars with points, although there are downsides to most of the retrofits on the market.
The next big change came in the late 70s and early 80s, when the engines now were effectively becoming computer controlled. Rather than having a distributor set the entire advance curve, a couple of sensors would feed information to a computer and let it decide the ignition timing. The two main sensors for this are the crank position sensor and the knock sensor. The CPS lets the computer know exactly where the engine is in the firing cycle, and the knock sensor detects engine knock. If the engine does knock, the computer retards the timing until it stops. The distributor was now reduced just to a mechanism to distribute the spark to the correct cylinder.
That is still putting a lot between the coil and the spark plug, so in the 90s manufacturers simplified things even more. Rather than having a single coil firing all cylinders, they started using "Coil Packs" that would feed directly into the cylinder. Sometimes, one coil would fire two plugs at the same time(wasted spark) to simplify parts.
Finally, in the late 90s, most manufactures eliminated the last problematic point-the high tension wires-and started putting the coils directly on the spark plugs(coil on plug).
Of course, that timeline is VERY general, and you can find later or earlier examples of the technologies I mentioned. I remember working on a friend's 97 Geo Prizm(Corolla) for example that had a distributor with the coil integrated. Toyota wanted you to swap the whole distributor rather than replace the coil, but I opted to brave the coil considering that it was a $40 part rather than $250 on a $500 car. There are also some competing ignition types that were dominant in specific application(magnetos come to mind, which were used in Model Ts, some racing engines, small engines, and of course are super common in aviation).