The physics of non-zero temperature dynamics and transport near quantum-critical points is discussed by a detailed study of the O(N)-symmetric, relativistic, quantum field theory of a N-component scalar field in d spatial dimensions. A great deal of insight is gained from a simple, exact solution of the long-time dynamics for the N = 1 d = 1 case: this model describes the critical point of the Ising chain in a transverse field, and the dynamics in all the distinct, limiting, physical regions ...