As the gases pass through the filter, the DPF will begin to get clogged with the soot that it has trapped. (Soot is a by-product of incomplete combustion - when the mixture of air and fuel that powers the engine fails to completely ignite). As the temperature of the exhaust gets higher, the residue heats up and turns to ash which is then expelled. This is called 'regeneration'. However, this will only happen when you travel at a speed greater that 40mph or when the engine raises the exhaust temperature artificially every 300 miles.
Some newer models of cars (from 2015 onwards) can use a Selective Catalytic Reduction (SCR) system. The system uses a liquid solution called AdBlue, also known as Diesel Exhaust Fluid (DE), which is made of a combination of water and urea and causes a chemical reaction in the exhaust system. This reaction converts the nitrogen oxides into water and nitrogen, reducing harmful exhaust pipe emissions.
However, this system is not a replacement for a DPF, since cars with AdBlue tanks will always feature a DPF as part of the overall control of emissions.