We present univariate and multivariate spatial functional predictors and their corresponding optimal sampling designs criteria. We derive unbiased predictors and the corresponding variances. In the univariate case, we propose to use a simple kriging predictor with the scalar random field resulting from the scores associated to the representation of the functional data with the empirical functional principal components. In the multivariate case, we develop spatial prediction of a functional variable at unsampled sites, using functional covariates; that is, we present a functional cokriging method. We show that through the representation of each function in terms of its empirical functional principal components, the functional cokriging only depends on the autocovariance and cross-covariance of the associated score vectors, which are scalar randomfields.