The recent development of a truly meshless method by using radial basis functions will be reported in this talk. Applications to both multivariate interpolation and solving partial differential equations have demonstrated the spectral convergence of the method for some particular radial basis functions like multiquadric. The ill-conditioning problem arises from solving the full resultant matrix, however, is still needed to be tackled. This talk will discuss some of the recent proposed techniques including the transformation of the original matrix into a Toeplitz matrix structure for faster matrix solver.