Atomically thin materials offer a new paradigm for control of electronic excitations in the extreme two-dimensional (2D) limit in condensed matter. Recently this concept has been developed further when artificial potentials for electrons were created in heterostructures consisting of stacked 2D layers held together by van der Waals forces, and light was used to access and manipulate electronic spin and valley degrees of freedom in atomically-thin semiconducting transition metal dichalcogenides (TMDCs). A significant world-wide effort in the last 5 years has resulted in intense studies of optical properties of TMDC atomic layers in the linear regime. Here, we propose to use this new class of (2D) semiconducting crystals to demonstrate unexplored approaches to exploiting nonlinear optical phenomena on the nano-scale in regimes unattainable by other ultra-fast photonic materials. To achieve this, we will exploit robust excitonic complexes observable up to room T, which will be generated and controlled in artificially created vertical stacks of 2D atomic layers. Giant nonlinearities enabling ultra-fast control of light with light of low intensity will be realised and explored in such van der Waals heterostructures placed in optical microcavities, operating in the strong light-matter coupling regime that we demonstrated recently. In this regime part-light-part-matter polaritons are formed, with the exciton part responsible for the strong nonlinearity and the photon part providing efficient coupling to light. This work will open a new route to development of highly nonlinear nano-photonic devices such as miniature ultra-fast modulators and switches, with high potential to impact on a new generation of signal processing and quantum technology hardware.