  In the field of atomically thin 2D materials, oxides are relatively
unexplored in spite of the large number of layered oxide structures amenable to
exfoliation. There is an increasing interest in ultra-thin film oxide
nanostructures from applied points of view. In this perspective paper, recent
progress in understanding the fundamental properties of 2D oxides is discussed.
Two families of 2D oxides are considered: (1) van der Waals bonded layered
materials in which the transition metal is in its highest valence state
(represented by V$_2$O$_5$ and MoO$_3$) and (2) layered materials with ionic
bonding between positive alkali cation layers and negatively charged transition
metal oxide layers (LiCoO$_2$). The chemical exfoliation process and its
combinaton with mechanical exfoliation are presented for the latter. Structural
phase stability of the resulting nanoflakes, the role of cation size and the
importance of defects in oxides are discussed. Effects of two-dimensionality on
phonons, electronic band structures and electronic screening are placed in the
context of what is known on other 2D materials, such as transition metal
dichalcogenides. Electronic structure is discussed at the level of
many-body-perturbation theory using the quasiparticle self-consistent $GW$
method, the accuracy of which is critically evaluated including effects of
electron-hole interactions on screening and electron-phonon coupling. The
predicted occurence of a two-dimensional electron gas on Li covered surfaces of
LiCoO$_2$ and its relation to topological aspects of the band structure and
bonding is presented as an example of the essential role of the surface in
ultrathin materials. Finally, some case studies of the electronic transport and
the use of these oxides in nanoscale field effect transistors are presented.
