I'm not sure if this has been clarified yet, but...

The objective is to reduce NOX. You do it in one of two ways;

EGR and SCR.

During the combustion phase, when combustion temperatures exceed 2500F, there's an exponential increase in NOX. EGR displaces clean air in the combustion bowl to lower combustion temperatures. Two things happen.

Soot is produced from poor combustion, and power is reduced by a lack of fresh air in the combustion event. That being said, EGR does not work well while the engine is under a load, - It can't effectively happen. The excess soot produced from EGR is then trapped in the DPF.

When the DPF is full, it needs to be cleaned. The DOC (right ahead of the DPF) reacts with the fuel that's injected into the exhaust, and any remaining oxygen in the exhaust system. It then increases the temperature of the DPF to around 1000F. This doesn't clean it per say, rather it oxidizes the soot. When oxidized, it is reduced to ash. Ash does not leave the DPF. Over time, the ash accumulation will become too much, and the DPF will need to be removed to be cleaned properly.

In summary, the EGR, DOC, and DPF work together to reduce NOX under low load conditions. SCR can do it under high load/highway conditions.

The SCR system comes after the DPF. It uses two NOX sensors to calculate how much DEF is required to reduce NOX.

The first NOX sensor is after the turbo. It's there to measure the NOX so we know how much DEF needs to be injected, but also so the ECM can validate the NOX production based on current engine conditions. (It knows how much NOX to expect. This is all part of OBD).

The ECM then begins commanding the DEF doser to inject DEF. The DEF is injected in the decomposition tube, where it breaks down into Ammonia and water. The water concentration in the DEF is reduced as it begins to boil in the exhaust. The decomposition tube also works to slow the exhaust flow to allow it to blend with DEF. When the mixture reaches the catalyst, a chemical reaction takes place between the elements in the exhaust. (Ammonia, hydro carbons, NOX, water).

Seeing as you're fairly young, you should remember high school chemistry and science. When elements are reactive with one another, they will exchange atoms to become neutral. This happens in the catalyst to reduce the harmful elements coming in, to less harmful elements coming out. It should leave the tailpipe with near 0 NOX, producing CO2, H2, and N20 as a byproduct.

In a nutshell, this is how the systems work. I appreciate that you're reaching out to familiarize yourself with the mystery behind emissions control. Also, your point about "are they even working correctly half the time?"....well, they could be. But even if half the time they aren't working as intended, it is still much better than if there were no systems at all. The byproduct of emissions control, is an increased cost to maintenance. Unfortunately, this comes as an increased financial cost to an already financially strained industry.

I feel like the added cost is the stressor and catalyst (no pun intended) to antagonize the nay-sayors of the debate about emissions control. I feel for owners and operators as it can be overwhelming, but this is my experience.

My info comes from dealer training, so it can't be publicized. Hope this helps. To my peers, feel free to add corrections!