In this talk we argue that prediction is a general statistical inference problem, which covers estimation and many non-standard inference problems as special cases. In the general set up, inferences are to be made about an unknown quantity z based on an observable random vector Y. The unknown quantity z may be fixed, or the realized but unobserved value of a random variable Z. In a parametric set up the joint density is assumed to be f_\theta(y, z), where \theta is an unknown parameter vector. In this context, we discuss minimum mean squared error (MSE) unbiased prediction of Z based on Y, and its relationships to minimum variance unbiased estimation of the expected value of Z. A Rao-Cramer type lower bound for the MSE of an unbiased predictor and some of its extensions and implications will be discussed. We shall present a characterization of uniformly minimum MSE unbiased predictors (UMMSEUP), and some interesting conclusions. Bayesian inferences and some decision theoretic results will be reviewed. Some applications of the results to prediction in mixed linear models, and estimation of the mean of a finite population under a super population model will also be discussed.