Static and dynamic behaviour of molecules under controlled confinement comparable with quantum-mechanical size of atoms is of particular interest in diverse areas of physics and biology. Molecules inside atomically thin nanocapillaries are anticipated to have enhanced interactions within them as well as with the capillary walls. Such confinement induced effects have big implications in the emergence of novel nanofluidic phenomena with interesting applications. Ultimate but seemingly distant goal of achieving atomically thin nanocapillaries has become feasible with systematic assembly of two-dimensional (2D) materials. The present talk demonstrates a methodical design of highly dense and uniform graphene nanocapillaries with variable sub-nm interlayer spacing. Molecular flow dynamics inside these capillaries will be discussed in terms of water and ion transport based on a series of bench-scale laboratory experiments with a prospect for desalination and smart membrane applications. Further, the profound impact of very high van der Waals pressure on the trapped molecules at atomically thin and smooth graphene interfaces will also be presented. Finally, I will discuss the experiments that are currently underway along with a proposed research.