Logarithmic operators and logarithmic conformal field theories

Logarithmic operators and logarithmic conformal field theories are reviewed. Prominent examples considered here include c = −2 and c = 0 logarithmic conformal field theories. c = 0 logarithmic conformal field theories are especially interesting since they describe some of the critical points of a variety of longstanding problems involving a two dimensional quantum particle moving in a spatially random potential, as well as critical two dimensional self-avoiding random walks and percolation. Lack of classification of logarithmic conformal field theories remains a major impediment to progress towards finding complete solutions to these problems. (review)