<p indent="0mm">Confined and interfacial water/ice is ubiquitous in nature and plays an important role in a broad range of physicochemical phenomena and technological processes such as rock fracture, friction, and nanofluids. The highly confined environment at the nanoscale can disrupt the hydrogen bonding network in water, thereby increasing the number of possible polymorphs of two-dimensional (2D) water/ice. It is also known that water molecules next to a solid surface can undergo stratification that extends two to three molecular diameters. A number of recent studies have revealed the possibility of forming 2D ice without the need of nanoscale confinement. For example, the presence of an ice-like water layer has been detected in scanning polarization force microscopy on the hydrated muscovite surface at room temperature. A sum-frequency generation experiment revealed no free OH bonds in the adsorbed water layer on mica. Scanning tunneling microscopy imaging evidence of a helical ice monolayer in which every six water molecules are helically arranged along the normal to the basal plane has reported. In addition, the growth of 2D bilayer hexagonal ice (BHI) structures has been widely observed on different surfaces, such as graphene, Pt(111) substrate, Ru(0001) substrate and Au(111) substrate, without the need of confinement in the laboratory. In this paper, we review the recent theoretical progress on the formation and growth of 2D ices without confinement. In particular, we focus on the important role of surface wettability and surface structure in the formation of 2D ices. We find that BHI formation on various surfaces and the dependence of the 2D crystalline structure on the hydrophobicity and morphology of the underlying surface. The tendency toward the formation of BHI without confinement reflects a proper water-surface interaction that can compensate for the entropy loss during the freezing transition. Moreover, both experiments and simulations show that armchair-type edges coexist with the zigzag edges in BHI. In the case of zigzag edge of BHI whose growth processes follow a collective bridging mechanism, a periodic but unconnected array of pentagons is initially formed at the zigzag edge, and subsequent incoming water molecules collectively connect these pentagons, resulting in a 565-chain structure. The addition of further water molecules leads to the formation of a fully connected hexagon array. By contrast, armchair edge growth involves edge reconstruction into a periodic structure of 5756-type membrane rings. Addition of two water pairs converts the 575-type member rings to 656-type member rings. The 656-type member rings then grow laterally to form a 5656-type edge. Further, inserting one water pair into the hexagon of the 5656-type edge leads again to the formation of a 5756-type edge. At low temperature, BHI forms only on the hydrophilic surface and not on the hydrophobic surface. Because of the close lattice match between the BHI and the ice <italic>I</italic><sub>h</sub> basal face, the orientation of the ice crystal on the hydrophilic surface is dictated by the preexistence of the BHI. Ice growth is anisotropic. Among the three prism crystal faces of ice <italic>I</italic><sub>h</sub>, namely, basal face (BF), prism face (PF) and secondary prism face (SPF), the growth of the BF is the slowest. For the hydrophilic surface, because the SPF and PF are perpendicular to the solid surface, the ice crystal grows along the surfaces. By contrast, for the hydrophobic surface, an angle is observed between the solid surface and SPF, indicating that the ice crystal grows off the solid surface.