The particulate filter is not only on Dodge trucks. GM and Ford trucks use a very similar system. Basically its a catch tank in the exhaust that collects all the soot from the exhaust. There are sensors that tell the engine computer when it gets full. When its full the engine fires the injectors on the exhaust stroke, which burns off the soot in the DPF (Diesel particulate filter)
The downsides are, that soot burns off and becomes ash which settles to the bottom. Somewhere around 100k the DPF will no longer be able to store all that soot and will need to be replaced.
Fuel economy goes down when it is dumping fuel down the tail pipe.
It will fill the DPF up much faster in around town, heavy footed, long idle, or engine modifications.
The computer will not alow it to go into REGEN (when it dumps fuel to burn off soot in the DPF) at low speeds or idle since it gets so hot. Truck needs to be moving somewhere above 35mph to cool the exhaust. Also the exhaust coming out the tailpipe can be over 500 degrees. Which is why each manufacturor has some sort of weird looking outlet, they are designed to help cool the output exhaust.That outlet is technically an emissions control device, so technically it can't be changed. Although I have seen plenty of aftermarket exhaust systems for these trucks already.