Publisher Summary This chapter discusses the theory of cross correlation and coherence along with their applications. The cross correlation refers to an indirect and un-defined relationship between the input and output of a system. In general a relationship can exist between any two signals whether or not they are intrinsically related through a system. It describes the various properties of these cross correlation functions. Such a function has symmetry properties that depend on the ordering of the two signals. Further, it explores the various fields where it can be used. A major implementation of cross correlation is for detecting the occurrence of time limited signals. These signals can have a random or deterministic nature. The basic concepts related to cross correlation are formulated in the chapter. Cross spectral density functions are introduced in detail providing definition and properties of the same. Finally, the last section of the chapter outlines tests for correlation between time series. Herein, the coherence estimators, statistical properties of estimators, confidence limits, procedure for estimation, and application are explored.