The fluctuations generated by chemical reactions may be observed in at least one of two ways: firstly by determining the autocovariance function or the power spectral density of the appropriate variable assuming stationarity; secondly as the statistics of ensembles of transients. Measurements on electrochemical systems using both approaches are illustrated with the following examples: (i) the two-dimensional nucleation and crystal growth of metals; (ii) the two-dimensional nucleation of pores in lipid bilayers; (iii) the three-dimensional nucleation and crystal growth of metals and semiconductors; (iv) the kinetics of electrocatalysis. It is shown that for many systems a single molecular event leads to a large realizable fluctuation especially if the size of the system being investigated is made small. The kinetic information which may be obtained from quantities related to the second (and higher) moments of the reaction rates is delineated.