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I discuss three new methods for the quantum many-body problem. The first is the pinhole trace algorithm for first principles calculations of nuclear thermodynamics. I will present lattice Monte Carlo results for the liquid-vapor critical point. The second is the eigenvector continuation method for extrapolation and interpolation of quantum wave functions. I will show how it can be used as a fast emulator for quantum many-body calculations and as a resummation method for divergent perturbative expansions. The third is the projected cooling algorithm for quantum computers. This method is able to construct the localized ground state of any Hamiltonian with a translationally-invariant kinetic energy and interactions that vanish at infinity.