Some of most difficult theoretical challenges in strongly-interacting many-body systems are concerned with transport. This involves understanding quantities such as the electric resistivity, the thermal conductivity, the viscosity, spin diffusivity etc. of media as diverse as the quark-gluon plasma, unconventional metals and cold atomic gases. I will argue that a handle on these problems can be gained from understanding fundamental limits on the dynamics of many-body systems imposed by quantum mechanics and statical mechanics themselves. The advantage of this approach is that it does not depend on the presence of weakly interacting quasiparticles.