A variety of recent advances in single-molecule methods are now making possible the routine measurement of the distinct catalytic trajectories of individual enzymes. Unlike their bulk counterparts, these measurements directly reveal the fluctuations inherent to enzymatic dynamics, and statistical measures of these fluctuations promise to greatly constrain possible kinetic mechanisms. In this chapter, we discuss a variety of advances, ranging from theoretical to practical, in the new and growing field of statistical kinetics. In particular, we formalize the connection between the hidden fluctuations in the kinetic states that compose a full kinetic cycle and the measured fluctuations in the time to complete this cycle. We then discuss the characterization of fluctuations in a fashion that permits kinetic constraints to be easily extracted. When there are multiple observable enzymatic outcomes, we provide the proper way to sort events so as not to bias the final statistics, and we show that these classifications provide a first level of constraint on possible kinetic mechanisms. Finally, we discuss the basic substrate dependence of an important function of the statistical moments. The new kinetic parameters of this expression, akin to the Michaelis-Menten parameters, provide model-independent constraints on the kinetic mechanism.