The Omicron variant of SARS-CoV-2 has rapidly become the dominant infective strain and the focus efforts against the ongoing COVID-19 pandemic. Here we report an extensive set of structures of the Omicron spike trimer by its own or in complex with ACE2 and an anti-Omicron antibody. These structures reveal that most Omicron mutations are located on the surface of the spike protein, which confer stronger ACE2 binding by nearly 10 folds but become inactive epitopes resistant to many therapeutic antibodies. Importantly, both RBD and the closed conformation of the Omicron spike trimer are thermodynamically unstable, with the melting temperature of the Omicron RBD decreased by as much as 7°C, making the spiker trimer prone to random open conformations. An unusual RBD-RBD interaction in the ACE2-spike complex unique to Omicron is observed to support the open conformation and ACE2 binding, serving the basis for the higher infectivity of Omicron. A broad-spectrum therapeutic antibody JMB2002, which has completed Phase 1 clinical trial, is found to interact with the same two RBDs to inhibit ACE2 binding, in a mode that is distinguished from all previous antibodies, thus providing the structural basis for the potent inhibition of Omicron by this antibody. Together with biochemical data, our structures provide crucial insights into higher infectivity, antibody evasion and inhibition of Omicron.