Harmonic analysis and probability have long enjoyed a mutually beneficial relationship that has been rich and fruitful. This monograph, aimed at researchers and students in these fields, explores several aspects of this relationship. The primary focus of the text is the nontangential maximal function and the area function of a harmonic function and their probabilistic analogues in martingale theory. The text first gives the requisite background material from harmonic analysis and discusses known results concerning the nontangential maximal function and area function, as well as the central...