How much has human domestication of various animals effected their natural track of evolution?

For example, let's use the most common- dogs and cats - have these animals not evolved or because of domestication, evolved differently?

This could extend to other domesticated animals that humans use for everyday things

Horses
Cows
Pigs
Chickens

The list goes on.

The effects of domestication on both plants and animals have been profound, but evolution has certainly not stopped. Domestication is a process of evolution, where the major selective pressure is towards phenotypes of benefit to humans, often called artificial selection. All domesticated species have been altered genetically to some degree, primarily by breeding control. The traits emphasised are typically yield of a particular product, such as large ears in maize, continuously growing wool on sheep and large size for meat animals. These traits are often emphasised to the detriment of others. For example, mModern corn, which was developed from a plant called teosinte, is unable to reproduce on its own and requires human intervention. Cattle and horses are virtually exclusively bred via artificial insemination.

The relationships between domestic animals and plants may seem to give the impression that they circumvent the processes of natural evolution, but a quick look around our biosphere can pick out many examples of mutual cooperation between organisms. The comparison is more obvious when you consider that farming an animal like a cow is actually a mutually beneficial relationship: the animal is protected from predators, is provided with food and water and reproduction is extensively assisted. In return the human farmers get food and a livelihood. There is some truth to the notion that instead of humans domesticating the wheat/dogs/corn/rice, those organisms have done a good job of coopting humans as a dissemination and propagation mechanism!

In short, not only have the domesticated species been in some cases drastically altered, but humans have also adapted as well. Evolution goes on regardless.