The quasiparticle concept is the foundation of our understanding of the dynamics of quantum many-body systems. It originated in the theory of metals, which have electron-like quasiparticles; but it is also useful in more exotic states like those found in fractional quantum Hall systems. However, modern materials abound in systems to which the quasiparticle picture does not apply, and developing their theoretical description remains one of the most important challenges in condensed matter physics. I will describe recent progress in understanding the dynamics of two systems without quasiparticles: the superfluid-insulator transition of ultracold atoms, and the `strange metal’ found in the high temperature superconductors. Some of this progress relies on holographic methods which map non-quasiparticle quantum systems to the dynamics of black hole horizons.