The complete work consists of a two-volume set, describing two main classes of non-equilibrium phase-transitions, and surveys two main aspects of non-equilibrium phase-transitions: (a) transitions in the steady-state and (b) transitions in the relaxation behavior.Volume 1, Absorbing Phase Transitions, published in 2008, covered the statics and dynamics of transitions into an absorbing state.This volume 2 covers dynamical scaling in far-from-equilibrium relaxation behaviour and ageing. Motivated initially by experimental results, dynamical scaling has now been recognised as a cornerstone in the modern understanding of far from equilibrium relaxation. Dynamical scaling is systematically introduced, starting from coarsening phenomena, and existing analytical results and numerical estimates of universal non-equilibrium exponents and scaling functions are reviewed in detail. Ageing phenomena in glasses, as well as in simple magnets, are paradigmatic examples of non-equilibrium dynamical scaling, but may also be found in irreversible systems of chemical reactions. Recent theoretical work sought to understand if dynamical scaling may be just a part of a larger symmetry, called local scale-invariance. Initially, this was motivated by certain analogies with the conformal invariance of equilibrium phase transitions; this work has recently reached a degree of completion and the research is presented, systematically and in detail, in book form for the first time. Numerous worked-out exercises are included. Quite similar ideas apply to the phase transitions of equilibrium systems with competing interactions and interesting physical realisations, for example in Lifshitz points.Aimed at researchers and graduate students in physics, the book is also suitable supplementary reading for advanced undergraduate students.