I've read gasoline engines use sparks to ignite the mixture, but diesel engines use just compression which can't be done in gasoline engines due to high compression ratios which can cause engine knocking, but if that was true gasoline? It can then be put in diesel engines and will ignite properly because diesel engines have high compression ratios, so why can't this be done?
And also diesel can be put in gasoline engines since they have a lower autoignition point?
You can run gasoline in a diesel motor, but it causes problems. As mentioned elsewhere, when you compress the fuel/air mixture enough, it gets really hot then ignites. With diesel, this is ok, because the fuel burns (relatively) slowly, so it doesn't need to be timed very well.
Gasoline, on the other hand, burns really fast. If you consistently ignite the fuel a little too early, you'll blow holes in your pistons, break piston rings, break connecting rods, shatter crankshafts, blow head gaskets, etc. If you ignite it just a little too late, it won't ignite at all.
The timing is based on the heat inside the combustion chamber, which changes constantly. So it's much harder to get the perfect timing. Even if it doesn't damage anything (diesel engines are much sturdier than a similar gasoline engine), the early ignition means your flame front is working against the piston for the last few degrees and wastes a significant amount of energy. You could probably put knock sensors in the head and add extra fuel to keep the temperature down, but that would be much harder on the conventional carbureted engines that got the current design started.*
Similarly, you can run diesel in a gasoline motor, but it's not very efficient (if you can keep it running at all). The high compression of a diesel motor helps the diesel fuel burn better (diesel is hard to burn), and the high compression of the injection pumps helps vaporize the fuel (if you pour it down the intake it tends to stay in liquid form which doesn't burn well). Without those things, you're only going to extract a fraction of the available power from the fuel.
.* Note that this is a large part of the answer: Just because we can do something now with modern technology doesn't mean they could a hundred years ago. Now that we have a hundred odd years doing it one way, there's no reason to make radical changes now without a significant advantage to using the new method.
You "can" use diesel in a gasoline engine. In the sense that it will run, but it will run poorly and smoke A LOT.
But the problem with gasoline in a diesel engine is that diesel engines rely on diesel to lubricate various components (diesel is an oil). If you put petrol through these components, it washes away all the lubrication and will cause them to overheat, seize up and fail.
As an aside, you can also run a diesel engine on cooking oil or parafin.
I would say there are two major reasons.
First, the seals and o-rings used in diesel engines can't tolerate the chemical composition of gasoline. They are designed to tolerate the chemical composition of diesel only.
Second, the kind of pressure needed to inject diesel can't be tolerated by gasoline. The Chevy Duramax diesel engine has 23,000 PSI in the fuel injection rail. This is compared to the Mazda DISI engine with direct fuel injection having rail pressure of 1,600 PSI. I dare to say that if there was even the slightest amount of air in a fuel line, gasoline would explode at those kind of pressures.
Edit
Diesel engines have very high compression. Because fuel is injected when the compression is very high, very high fuel pressure is required (it also helps atomization). A modern diesel engine like the Chevy Duramax has a fuel pressure of 23,000 PSI in the fuel rail. The closes comparison is a direct injected gasoline engine. Direct injection refers to the fuel being sprayed directly into the cylinder similar to the diesel instead of the fuel being sprayed in on top of the intake valve like most regular gasoline engines. A modern direct injected gasoline engine like the Mazda DISI (direct injected spark ignition) has a fuel rail pressure of only 1,600 PSI, more then ten times less the the comparable diesel engine. Gasoline is not meant to tolerate the pressure that a diesel engine can produce.
You can see the ill-effects of misfueling in this episode by Fifth Gear.
They put petrol (gasoline) in a diesel car and vice versa.
A summary of the differences between the two fuels:
Diesel does not burn as easily as petrol. It relies on auto-ignition under compression rather than spark-ignition to combust.
Diesel has a higher AFR value than petrol.
Diesel is injected at significantly higher pressures than petrol.
Diesel engines have a higher compression ratio than petrol engines.
Diesel has better lubricating properties than petrol.
These differences are the key reasons behind why the petrol engine in the video misfired so badly when it ran on diesel; the fuel just won't readily combust in a petrol engine. With enough time, the catalytic converter(s) will get clogged with unburnt diesel.
In the case of the diesel engine, petrol will run because it auto-ignites under the extreme pressures of the diesel combustion chamber. The damage here has less to do with how the car runs and more to do with long-term damage to the components along the fuel line.
The other posters have answered your question well, but I'd like to add that diesel engines can burn spark-ignition fuels under certain circumstances. Large industrial diesel engines can run on natural gas with some minor modifications. However, they still need a small amount (about 1%) of diesel blended in.
The diesel ignites under compression and essentially provides the "spark" for what is normally a spark-ignition fuel.
Gasoline could be used in a similar setup, but fraction of diesel required will be in flux. Something like 50% at low load, and 25% at high load. Not to mention that extensive monitoring will be needed to control injection to avoid knocking.
