Recently a consistent modification of general relativity was discovered. This theory describes nonlinear self-interactions of a massive spin-2 field and avoids the notorious ghost instability that generically arises when gravity is modified by the addition of a mass term. The formulation of such a massive gravity theory requires a second rank-two tensor (or metric), which naturally leads to a generalization of the setup to a bimetric theory of gravity. Ghost-free bimetric theory includes dynamics for the second rank-two tensor and describes the nonlinear interactions of a massive and a massless spin-2 field. In this talk, I will give a basic introduction to these novel consistent field theories and provide the main arguments for the absence of the ghost mode. Furthermore, I will discuss a particular choice for the parameters in the interaction potential which is believed to give rise to an additional gauge redundancy in bimetric theory. The corresponding gauge transformation is a nonlinear extension of the symmetry for partially massless spin-2 fields in a de Sitter background. Interestingly, this particular bimetric model is closely related to the well-studied theory of conformal gravity but, unlike the latter, it is free of ghosts.