In the search of a fusion reactor using magnetic confinement of toroidal plasmas, many important plasma performance parameters directly depend on the shape of the plasma cross-section. The unique shaping capability of the TCV tokamak ("Tokamak à Configuration Variable") has been exploited to study different aspects of tokamak transport and stability, in which the plasma shape may play a role. This presentation will focus on the effects of plasma shape on transport. The TCV tokamak has produced a host of physics results on diverse topics such as core sawtooth instabilities, edge localised modes (ELMs), electron cyclotron heating (ECH) and current drive (CD), plasma control, MHD stability, internal transport barriers (ITB), innovative “snowflake” divertors. TCV can produce plasmas with extreme shapes, elongation κ up to 2.8 and both negative and positive triangularity δ from –0.8 to +1, and is equipped with 4.5MW of localized Electron Cyclotron Heating (ECH). A significant fraction of TCV results has benefited from plasma shaping. The characterization of the various effects of shaping serves essentially two purposes: 1) it provides stringent tests for theory, being thus a valuable tool for model validation, and 2) it is crucial for the design of a fusion reactor, since plasma shape has a marked influence on confinement, MHD stability and performance. As an example, confinement in TCV has been demonstrated to depend strongly on triangularity in low-collisionality L-mode plasmas, improving towards negative triangularity. For illustration, the heat flux necessary to sustain the same profiles and stored energy in a discharge with δ=-0.4 is only half of that required for a discharge with δ=+0.4. The observed dependences of the electron thermal diffusivity on triangularity (direct) and collisionality (inverse) are qualitatively reproduced by nonlinear gyro-kinetic simulations and shown to be governed by Trapped Electron Mode (TEM) turbulence. Both in the linear and non-linear phases, negative triangularity is found to have a stabilizing influence on the TEM by modifying the toroidal precessional drift of trapped electrons that resonantly drive the modes. Negative triangularity also enhances the local shear, which in turn increases the perpendicular wave number, thus reducing the mixing length transport estimate. Both heat transport measurements and gyro-kinetic simulations demonstrate the stabilising effect of electron-ion collisions, which is now further sustained by recent electron temperature turbulence measurements using correlation-ECE.