Good grief! Yes, we can communicate with animals! Why do you not know this. I have to guess that you have never had a pet.
Dogs can learn about 200 words. Most trainers equate dogs to have the intelligence of 2 or 3 year old kids.
Cats understand some words, but definitely know what time it is when it's time to be fed. They will let you know if you don't feed them at the right time. That is communication.
Horses and pigs are extremely communicative if you have the patience and empathy to understand them.
Dolphins and Whales and Elephants have massive brains, much bigger than our human brains. They do have a language and they communicate with each other very well. They also communicate with humans when it suits them.
The great apes can be taught sign language and they then communicate with their trainers, even forming whole sentences.
Birds obviously communicate with each other. They are flock animals and hundreds of them can make the same flight pattern as the others all at the same time.
Fish communicate like birds do. I have seen aquarium fish try to communicate with humans, especially at feeding times.
Reptiles seem to have primitive brains, but enhanced sensing organs. They can track their prey. This involves communication.
There is nothing magical about communication between species. I can talk to my dog or my cat and they can understand me.
Any animal that can learn commands is doing so via communication.
Humans are the only animals that have complete vocal chords that make hundreds of different sounds. Animals are more limited in vocalizations, but they do have them.