  By the early 1960's advances in statistical physics had established the
existence of universality classes for systems with second-order phase
transitions and characterized these by critical exponents which are different
to the classical ones. There followed the discovery of (now famous) scaling
relations between the power-law critical exponents describing second-order
criticality. These scaling relations are of fundamental importance and now form
a cornerstone of statistical mechanics. In certain circumstances, such scaling
behaviour is modified by multiplicative logarithmic corrections. These are also
characterized by critical exponents, analogous to the standard ones. Recently
scaling relations between these logarithmic exponents have been established.
Here, the theories associated with these advances are presented and expanded
and the status of investigations into logarithmic corrections in a variety of
models is reviewed.
