A number of nanomechanical experiments have recently reached the quantum regime. Many of these experiments are based on a linear optomechanical coupling between a nanomechanical resonator and a cavity, where the motion of the resonator changes the resonance frequency of the cavity. We have made such an optomechanical device consisting of a mechanical resonator inside an optical cavity formed between the ends of two optical fibers. I will discuss two different types of mechanical resonators. First, we have incorporated a silicon nitride membrane into the cavity and used light in the cavity to couple and transfer energy between two mechanical modes of the membrane. This is a first step towards realizing theoretical proposals for creating nonclassical mechanical states and storing quantum information. Second, I will describe our progress towards using a very different type of mechanical resonator and coupling the acoustic modes in superfluid liquid helium to the fiber-cavity.