Molecular machines transduce free energy between different forms throughout all living organisms. Unlike their macroscopic counterparts, molecular machines are characterized by stochastic fluctuations, overdamped dynamics, and soft components, and operate far from thermodynamic equilibrium. In addition, information is a relevant free energy resource for molecular machines, leading to new modes of operation for nanoscale engines. Toward the objective of engineering synthetic nanomachines, an important goal is to understand how molecular machines transduce free energy to perform their functions in biological systems. In this review, we discuss the nonequilibrium thermodynamics of free energy transduction within molecular machines, with a focus on quantifying energy and information flows between their components. We review results from theory, modeling, and inference from experiments that shed light on the internal thermodynamics of molecular machines, and ultimately explore what we can learn from considering these interactions.