Animals that understand Human Speech 

Some animals do understand human language by their actions, behaviour or even some of the words 

Dogs  According to a study in 2016, dogs can understand human speech and they even respond to it.

Potbelly Pigs  Scientists believe that even potbelly pigs have the capability to understand human speech.

Chimpanzee Chimpanzees understand some of the human speech and they sometimes respond to them also.

Elephant As surprising as it may be, but even elephants have the ability of understanding human speech. 

Dolphin  Scientists believe we may even be able to talk to dolphins some day.

Parrot  They understand human speech and can talk in full sentences as well.