Dense liquids above their glass transition exhibit spatially heterogeneous dynamics (SHD) in which regions within the liquid exhibit enhanced or diminished mobility relative to the average on some time scale. The spatially heterogeneous nature of local dynamics in supercooled liquids is fairly well established both experimentally and computationally. However, many questions remain concerning why and how this complex dynamics arises. Here we address these questions and present results of a detailed investigation of SHD in models of a one-component supercooled liquid and a low-molecular-weight polymer melt, via molecular dynamics simulation.

We find that particles or chain segments (monomers) with high mobility exhibit a correlated motion in which they move in a quasi-one dimensional ``string-like'' paths that aggregate into larger, ramified clusters. These dynamical clusters grow in size with decreasing temperature. The mean string and cluster sizes show a transient nature, with peaks at the late-$\beta$/early-$\alpha$ relaxation time of the mode-coupling theory (MCT). The size distribution of the strings shows an exponential behavior, while that of the clusters approaches a power law near $T_{\rm MCT}$. We further investigate the microscopic details of local particle dynamics in order to understand the mechanisms by which particles move along string-like correlated paths. We find that the degree of coherence, i.e., the simulataneous motion by consecutive particles along a string, depends on the length of the string.

We also explore the thermodynamic behavior of the one-component liquid via the inherent structure formalism to study the connection between the dynamical strings and clusters we have investigated and the ``cooperatively rearranging region (CRR)'' of the Adam-Gibbs (AG) theory. We find that the average cluster size is linearly related to the inverse of the configurational entropy $S_{\rm conf}$, as observed in simulated water. However, we also find a similar linear relationship between the average string size and configurational entropy.