  Logarithmic conformal field theories have a vast range of applications, from
critical percolation to systems with quenched disorder. In this paper we
thoroughly examine the structure of these theories based on their symmetry
properties. Our analysis is model-independent and holds for any spacetime
dimension. Our results include a determination of the general form of
correlation functions and conformal block decompositions, clearing the path for
future bootstrap applications. Several examples are discussed in detail,
including logarithmic generalized free fields, holographic models,
self-avoiding random walks and critical percolation.
