Pollution is a pretty fundamental concept in the game. Pollution has several negative side effects, including a reduced life expectation, a lower Mayor Rating and a lower desirability and thus abandonment. Therefore, you'll generally want to avoid pollution in your city.
However, because in practice this often isn't possible, it's best to rather confine pollution to a specific location. As pollution doesn't spread beyond the city borders, placing polluting industries and structures at a corner is an effective strategy at reducing pollution.
Air pollution is caused by quite many objects, including dirty and manufacturing industry, most power plants, airports, and also traffic. Note that the spread of air pollution is affected by the terrain, so building industries behind a mountain range, for example, will restrict the polluted air from moving beyond the mountains. You can use that to your advantage in God Mode by terraforming an industrial zone entirely enclosed by mountains.
Air pollution can be reduced by parks as well as trees (both the trees from God Mode and manually planted trees work fine). Some of the rewards, such as the cemeteries, are also effective ways of limiting air pollution. There are also a few ordinances that help reduce air pollution.
Water pollution is caused by industry, and very much by farms. Unlike air pollution, it isn't too much of a problem (although it has the same negative effects); note however that if the water pollution around your water towers or pumps is too high, they will be shut down, therefore build your water towers and pumps away from sources of water pollution by any means.
The only way to combat water pollution in the game is to build a water treatment plant, however due to their high cost and low capacity, it is not advisable to build them except in very rare cases.
Even though it's not noted as a separate type of pollution in the game, traffic pollution or traffic noise can also have negative side effects. Naturally, any ways of reducing the car traffic will lower traffic noise. Also try to route traffic through commercial areas, which are positively affected by high traffic.
Besides a few oddball rewards, there are two main sources of radiation: the Toxic Waste Dump business deal, and the meltdown of a nuclear power plant. Radiation is an absolute killer to desirability, nothing at all will grow in an irradiated area. While the radiation of a toxic waste dump will disappear soon after the building is demolished, radiation caused by a meltdown will stay for decades, and as there isn't a way to clean up radiation, after a meltdown it's usually best to just start over the city.