A statistical characterisation of clutter as a complex random process is needed in the design of optimum detection schemes. The paper considers modelling complex clutter as a spherically invariant random process (SIRP), namely assuming that its PDFs can be expressed as non-negative definite quadratic forms, a generalisation of a Gaussian process. Relevant properties of SIRPs are summarised, and shown to comply with basic requirements such as circular symmetry of the joint PDF of the in-quadrature components or, equivalently, the uniformity of the phase distribution. A constraint of admissibility must be imposed on the envelope distribution, but most commonly used envelope distributions, including Weibull, contaminated Rayleigh andK-distribution are shown to be admissible. Although a general SIRP is not ergodic, a characterisation of the clutter process as an SIRP scanned in the ensemble is finally proposed, which restores ergodicity. The interpretation of this model in the light of already proposed composite scattering models is also discussed.