We consider the classical problem of determining the spectral asymptotics for the Laplace operator on a bounded domain. Over 100 years ago Weyl established the leading order term for bounded domains in Euclidean space. In the setting where the boundary is smooth, the second order term can be calculated but in the non-smooth case, when the boundary is fractal, a range of behaviour is possible. I will consider this problem, and the asymptotics for related quantities such as the heat content, for domains with random fractal boundary and for domains which are themselves random fractals. Our aim will be to determine more detailed asymptotics in these settings.