Quantum field theory lies at the heart of both condensed-matter and high energy physics. In some parameter regimes, such as strong coupling, extracting quantitative predictions from quantum field theories, particularly regarding dynamical quantities such as scattering probabilities, appears to be intractable using conventional techniques. Here I will discuss new advances in quantum algorithms for simulating quantum field theories which achieve exponential speedup over known classical algorithms and polynomial speedup over prior quantum algorithms. This is joint work with Keith Lee, John Preskill, Hari Krovi, and Ali Moosavian.