Provided herein are polyfarnesenes such as farnesene homopolymers derived from a farnesene and farnesene interpolymers derived from a farnesene and at least a vinyl monomer; and the processes of making and using the polyfarnesenes. The farnesene homopolymer can be prepared by polymerizing the farnesene in the presence of a catalyst such as a Ziegler-Natta catalyst, a Kaminsky catalyst, a metallocene catalyst, an organolithium reagent or a combination thereof. In some embodiments, the farnesene is prepared from a sugar by using a microorganism.