The power spectrum of relative sea level change has been estimated over more than 15 orders of magnitude in frequency, from a frequency of 1/(591 Ma) to a frequency of 1/(5 s). Although there are still regions of the spectrum where data sampling and duration do not allow the power to be calculated, most notably between periods of 100--1000 years, the general shape of the spectrum is that in which the power depends on the square of the reciprocal frequency, apart from periods between 1 and 100 years where the power spectrum falls off less steeply with increasing frequency. A spectrum in which power depends on reciprocal frequency squared is the same spectrum as that calculated from a random walk signal of finite length. There are some causes that have defined frequencies, such as those associated with tides and the Milankovitch cycles of the ice ages, but there is also a continuum of relative sea level change that requires other causes. The implications of this are discussed in the light of global change and heating of the lithosphere from the bottom.