We develop a new theoretical model for the Kondo lattice. We find that the Kondo lattice is qualitatively different from a collection of independent impurities: The ground state is characterized by coherence in the effective hybridization matrix. The low-temperature excitations are heavy fermions. The interactions between heavy fermions mediated by fluctuations around the mean-field solution are weak but can be long ranged in the Kondo regime. As a result, the Kondo lattice is prone to instabilities which we discuss in the context of recent experiments.