Quasi-interpolation and interpolation with radial basis functions are the most often used methods of approximation in multiple space dimensions by shifts of kernel functions. The advantages of quasi-interpolation are manifold: they are suitable for smoothing for instance and allow function information not only to be provided by pointwise evaluation, but also by local integrals, divided differences etc. In this talk we shall speak about quasi-interpolation and convergence orders using shifts of radial basis functions, and we shall also mention a new method to approximate by radial basis functions with rational interpolants.