I will briefly explore the definition and limitations of the Cold Dark Matter (CDM) paradigm before introducing Generalised Dark Matter (GDM), an approach that subsumes the CDM paradigm. GDM facilitates well-defined model-independent observational constraints on the cosmological dark matter, including null tests of CDM. I will present some constraints that have been obtained using a combination of cosmological datasets, notably Planck, BAO and WiggleZ matter power spectrum data, including constraints on the equation of state and abundance of dark matter over 5 decades in redshift. An observational hint of beyond-CDM properties will be presented, along with a discussion of the importance of correctly modelling non-linear cosmological scales.