All optical fields are inherently of statistical nature undergoing random fluctuations. The underlying theory of fluctuating optical fields is known as coherence theory and partial polarization. This thesis describes the experimental study on the coherence and polarization measurements for statistical optical fields. Particular emphasis is placed on the full field visualization for coherence function and coherence matrix, and its application to the study of changes in random optical fields on propagation. The thesis consists of 9 chapters including Chapter 1 devoted to introduction. Chapter 2 proposes a novel optical geometry for the full-field coherence visualization to study the coherence diffraction. The non-diffracting solutions for the coherence function and the coherence interference phenomena have been presented in Chapter 3 and Chapter 4, respectively. As the application, Chapter 5 presents the experimental demonstration of the coherence holography to synthesize the arbitrary spatial coherence function. To take the vector nature, Chapter 6 and Chapter 7 develop our optical geometry for the full-field visualization of coherence polarization matrix to study of the stochastic electromagnetic fields on propagation. The principle of coherence tensor holography is proposed in Chapter 8 and experimentally demonstrated for the first time. At last, conclusions and future works have been given.