Since its emergence, the COVID-19 threat has been sustained by a series of transmission waves initiated by new variants of the SARS-CoV-2 virus. Some of these arise with higher transmissivity and/or increased disease severity. Here, we use molecular dynamics simulations to examine the modulation of the fundamental interactions between the receptor binding domain (RBD) of the spike glycoprotein and the host cell receptor (human angiotensin-converting enzyme 2 [hACE2]) arising from Omicron variant mutations (BA.1 and BA.2) relative to the original wild-type strain. Our key findings are that glycans play a vital role at the RBD···hACE2 interface for the Omicrons, and the interplay between glycans and sequence mutations leads to enhanced binding. We find significant structural differences in the complexes, which overall bring the spike protein and its receptor into closer proximity. These are consistent with and attributed to the higher positive charge on the RBD conferred by BA.1 and BA.2 mutations relative to the wild-type. However, further differences between subvariants BA.1 and BA.2 (which have equivalent RBD charges) are also evident: mutations reduce interdomain interactions between the up chain and its clockwise neighbor chain in particular for the latter, resulting in enhanced flexibility for BA.2. Consequently, we see occurrence of additional close contacts in one replica of BA.2, which include binding to hACE2 by a second RBD in addition to the up chain. Although this motif is not seen in BA.1, we find that the Omicrons can directly/indirectly bind a down-RBD to hACE2 through glycans: the role of the glycan on N90 of hACE2 switches from inhibiting to facilitating the binding to Omicron spike protein via glycan-protein lateral interactions. These structural and electrostatic differences offer further insight into the mechanisms by which viral mutations modulate host cell binding and provide a biophysical basis for evolutionary driving forces.