  We calculate the Polyakov loop susceptibilities in the SU(3) lattice gauge
theory using the Symanzik improved gauge action on different-sized lattices.
The longitudinal and transverse fluctu- ations of the Polyakov loop, as well
as, that of its absolute value are considered. We analyze their properties in
relation to the confinement-deconfinement phase transition. We also present
results based on simulations of (2+1)-flavor QCD on 32^3 x 8 lattice using
Highly Improved Staggered Quark (HISQ) action by the HotQCD collaboration. The
influences of fermions on the Polyakov loop fluctuations are discussed. We
show, that ratios of different susceptibilities of the Polyakov loop are
sensitive probes for critical behavior. We formulate an effective model for the
Polyakov loop potential and constrain its parameters from existing quenched
lattice data including fluctuations. We emphasize the role of fluctuations to
fully explore the thermodynamics of pure gauge theory within an effective
approach.
