The TCV tokamak facility is used to study the effect of innovative plasma shapes on core and edge confinement properties. In low collisionality L-mode plasmas with electron cyclotron heating (ECH) confinement increases with increasing negative triangularity δ. The confinement improvement correlates with a decrease of the inner core electron heat transport, even though triangularity vanishes to the core, pointing to the effect of non-local transport properties. TCV has recently started the study of the effects of negative triangularity in H-mode plasmas. H-mode confinement is known to improve towards positive triangularity, due to the increase of pedestal height, though plagued by increasingly large edge localised modes (ELMs). An optimum triangularity could thus be sought between steep edge barriers (δ > 0) with large ELMs, and improved core confinement (δ < 0) with small ELMs. This opens the possibility for a reactor of having H-mode-level confinement within an L-mode edge, or at least with mitigated ELMs. In TCV, ELMy H-modes with upper triangularity δtop < 0 are explored, showing a reduction of ELM peak energy losses compared to δtop > 0. Alternative shapes are proposed on the basis of ideal MHD stability calculations. Shaping has the potential to bring at the same time key solutions to confinement, stability and wall loading issues and, from the comparison of experimental and simulation results, to give deeper insight in transport and stability.