Abstract: The quasiparticle concept is the foundation of our understanding of the dynamics of many-body quantum 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 present an elementary description of two key models without quasiparticle excitations, both motivated by recent experiments. The first is the superfluid-insulator transition of ultracold bosonic atoms trapped in optical lattices in two spatial dimensions. Its low energy theory is a conformal field theory in 2+1 spacetime dimensions, and this fact allows us to gain insight from the AdS/CFT correspondence of string theory. The second model is the Pomeranchuk instability of two dimensional metals at which 90 degree lattice rotation symmetry is broken. Such an instability has been found to play a prominent role in many recent experiments on the high temperature superconductors in the vicinity of the "strange metal" regime. The Pomeranchuk critical point realizes a metal with a Fermi surface, but no sharp quasiparticle excitations. I will summarize our current understanding, which draws upon the methods of quantum field theory and holography. I will conclude with a perspective on the physics of the high temperature superconductors. The lectures will review key background material on Fermi liquid theory and the theory of phase transitions, and will not assume knowledge of string theory or the AdS/CFT correspondence. The Salam Distinguished Lecture Series are livestreamed and can be viewed at: https://www.ictp.it/about-ictp/media-centre/videos