A non-uniform deformation of a honeycomb medium induces effective-magnetic and effective-electric fields. One may choose a deformation which gives rise to a constant perpendicular effective-magnetic field with Landau-level spectrum (flat bands). In the setting of photonic crystals, the tight binding model is generally not applicable. I’ll present a continuum theory, and some rigorous and formal asymptotic results (joint work with J. Guglielmon and M. Rechtsman - Phys. Rev. A 103 2021), and then review very recent experimental confirmation of this theory (Barsukova et al. https://arxiv.org/abs/2306.04011).