In recent years there has been a flurry of interest in topological materials and in their exotic physics. Most of the developments in optics have been inspired in one way or other by the theory of condensed matter systems. However, photonic systems have a few peculiar features that are not found in their electronic counterparts. The first of such properties is related to the unavoidable material dispersion as the permittivity tensor depends on frequency. The second property is the particle-hole symmetry inherited from the reality of the electromagnetic field: the spectrum is formed by positive and negative frequencies. In this talk, we will show how the combination of the two properties leads to surprising situations and discuss how they tailor the topology of dispersive photonic platforms. In particular, we will present first principles calculations of the topological numbers of dispersive photonic crystals.