The (β,γ)-Chebyshev functions and points, which we studied recently, generalise the classical Chebyshev polynomials and related points, and can be employed effectively in polynomial interpolation tasks on the interval [-1,1]. On the other hand, unions of tensor-product Chebyshev grids provide sets of nodes that guarantee a stable polynomial interpolation process on the square [-1,1]^2, and that can be characterised as self-intersection or square-tangency points of Lissajous curves. Therefore, this paves the way for the study of (β,γ)-Chebyshev grids and for the analysis of polynomial approximation schemes along (β,γ)-Lissajous curves in [-1,1]^2, in view of designing a unified generalised framework. Joint work with Stefano De Marchi and Giacomo Elefante.