This is a really interesting question philosophically, because you first have to answer the question ‘What is language’. Language is learned and it can be used to express abstract ideas like “does god exist?” or “will there be a test on this book?”.
Research so far indicates that animals can communicate but its not true language. Animals are born knowing how to communicate. If a baby cries, it is communicating that it is hungry, but it isn’t using real language. Animals do the same thing.
Insects communicate very differently from humans. We mostly use writing, speaking and some facial expressions and gestures (like flipping someone the bird). Insects on the other hand have smells. Bees use smells (and dancing) to tell other bees where the best flowers are. Most insects use smells to attract a mate and show off how awesome they are to others. Queen ants, bees and termites use smells to control their workers. Imagine if you tried to attract a boyfriend by farting. 🙂 Thats how insects do it.
This is something that is really hard to answer because scientists are looking into this right now. A lot of scientists think dolphins and whales have some sort of language, for instance, and we can teach primates to use sign language, so they seem to have the capability. But other animals are also very capable of communicating thoughts using noises and gestures. Bats communicate to each other using sounds, for instance, but it doesn’t seem like it’s what we would call language.