There are several different emissions control technologies developed over the past 20yrs.
First is cleaner combustion through improved piston design and advanced fuel systems. Old mechanical pump/line direct fuel injection is replaced by HEUI, MEUI, and Common Rail electronically controlled direct injection. These advanced injections systems allow more flexibility for cold start, emissions reduction, high injection pressures, and more efficient combustion. The tradeoff is more complexity and very tight tolerances on a very high pressure system (150-300MPa = 21,700PSI - 43,500PSI). Good clean fuel, and regular high quality fuel filter changes are a must.
Additional improvement is found in the turbo design and charge air cooling design. Higher boost and lower charge air temps are an important building block for reduced emissions. Not only have turbos gotten significantly more efficient and better matched to engines, but some manufacturers have added complex controls like Variable Geometry Turbines (VGT) and Variable Nozzle Turbine (VNT).
More recently, Exhaust Gas Recirculation (EGR) has been added. This affects the chemistry of combustion and also reduces emissions dramatically, with improvement to fuel economy. The downside is increased soot load in the engine oil. Improved fuel refinement and better oils help mitigate this tradeoff. Low Sulfur and Ultra Low Sulfur Diesel (ULSD) is important to help an EGR engine last. The sulfur in diesel fuel can burn creating SO2, which turns into sulfuric acid in the presence of water (exhaust). Recirculating sulfuric acid through an engine is not good. Use ULSD to help reduce this harm.
Also recently added are after-treatment systems. This means chemically processing the exhaust coming out of the turbo. In this category are DPF, DOC, SCR and AMOx.
DPF = diesel particulate filter - captures PM in a filter. The PM is oxidized to CO2 either by dosing with additional raw fuel injection into exhaust or heating to high temp with a burner or heating to high temp by a heavy load on the engine.
DOC = diesel oxidation catalyst - continuously reacts the HC to CO2 and H2O. This is a precious metal catalyst, much like a 3-way catalyst in a car. DOCs require Low Sulfur fuels to prevent fouling of the catalytic surface.
SCR = selective catalytic reduction - a combination of catalyst and another substance, urea. When heated by the exhaust the urea converts to ammonia and reacts with NOx to reduce it to N2 and H2O on the surface of this catalyst.
AMOx = ammonia oxidation - a catalyst to catch any ammonia slipping by the SCR system and convert down to harmless N2 & H2O.