  We report an extensive and systematic investigation of the multi-point and
multi-time correlation functions to reveal the spatio-temporal structures of
dynamic heterogeneities in glass-forming liquids. Molecular dynamics
simulations are carried out for the supercooled states of various prototype
models of glass-forming liquids such as binary Kob-Andersen, Wahnstrom,
soft-sphere, and network-forming liquids. First, we quantify the length scale
of the dynamic heterogeneities utilizing the four-point correlation function.
The growth of the dynamic length scale with decreasing temperature is
characterized by various scaling relations that are analogous to the critical
phenomena. We also examine how the growth of the length scale depends upon the
model employed. Second, the four-point correlation function is extended to a
three-time correlation function to characterize the temporal structures of the
dynamic heterogeneities based on our previous studies. We provide comprehensive
numerical results obtained from the three-time correlation function for the
above models. From these calculations, we examine the time scale of the dynamic
heterogeneities and determine the associated lifetime in a consistent and
systematic way. Our results indicate that the lifetime of the dynamical
heterogeneities becomes much longer than the alpha relaxation time determined
from a two-point correlation function in fragile liquids. The decoupling
between the two time scales is remarkable, particularly in supercooled states,
and the time scales differ by more than an order of magnitude in a more fragile
liquid. In contrast, the lifetime is shorter than the alpha-relaxation time in
tetrahedral network-forming strong liquid, even at lower temperatures.
