The curvature of soft interfaces plays a crucial role in determining their mechanical and thermodynamic properties, both at macroscopic and microscopic scales. In the case of air/water interfaces, particular attention has recently focused on water microdroplets, due to their distinctive chemical reactivity. However, the specific impact of curvature on the molecular properties of interfacial water and interfacial reactivity has so far remained elusive. Here, we use molecular dynamics simulations to determine the effect of curvature on a broad range of structural, dynamical, and thermodynamical properties of the interface. For a droplet, a flat interface, and a cavity, we successively examine the structure of the hydrogen-bond network and its relation to vibrational spectroscopy, the dynamics of water translation, rotation, and hydrogen-bond exchanges, and the thermodynamics of ion solvation and ion-pair dissociation. Our simulations show that curvature predominantly impacts the hydrogen-bond structure through the fraction of dangling OH groups and the dynamics of interfacial water molecules. In contrast, curvature has a limited effect on solvation and ion-pair dissociation thermodynamics. For water microdroplets, this suggests that the curvature alone cannot fully account for the distinctive reactivity measured in these systems, which are of great importance for catalysis and atmospheric chemistry.