Regression using certain basis function (i.e. find coefficients for a certain linear combination of these that fits the training data). Standard ones are polynomials (see Weirestrass approx theorem, but possible terms become very large as we increase degree).
Can also use Gaussians, or radial basis functions (RBFs).
Once kernel functions are used, then can use same methods as for linear regression. Basically, we replace each input datum with the kernel functions evaluated at the input datum.