Thus far, we have discussed the propagation of regular waves which exhibit only a single amplitude and frequency. Fortunately, our real world is not quite so boring and purely regular waves rarely occur in nature. As an example, when gazing upon the waves in Sydney Harbor, we can clearly observe the seemingly random patterns that characterize a more realistic sea state. Irregular waves are produced from the superposition (i.e., linear summation) of individual sinusoidal wave components across a wide range of amplitudes and frequencies. This chapter will introduce the statistics of irregular waves and their treatment in both time and frequency domains.