Statistics and probability theory complement each other, so do statistical framework and probabilistic framework. This chapter begins with an overview of statistical framework, including statistics and statistical learning. Secondly, we review the two component of classic statistics, namely, descriptive statistics and inferential statistics. We next introduce two statistical inference methods in mathematical statistics, namely, frequentist inference and Bayesian inference. This chapter then discusses statistical learning theory, where statistical models are the cornerstone of statistical learning theory, statistical learning models are the core of statistical learning theory, and growth functions, VC dimension, and Rademacher complexity are the components of statistical learning theory. Parametric and nonparametric models, as well as kernel methods, are also important components of statistical frameworks, and they are detailed in the last two sections of this chapter.