In this talk two new sub-classes of photonic bandgap materials, a) curvilinear-lattice photonic crystals, whose distinctive feature is that their individual scatterers are arranged in a curvilinear lattice and b) variable size photonic bandgap structures are introduced. We show that adhering to some restrictions in the acceptable lattice transformations, one can achieve omni-directional photonic bandgaps for the whole area of such structures. We demonstrate, designing an efficient waveguide bend, that curvilinear-lattice photonic crystals can be employed for creation of original types of nano-photonic devices. For variable size photonic bandgap structures the effects of geometrical parameter variation on the properties of photonic crystals is studied. We show that long-range periodicity is not necessary for the formation of bandgaps, which leads to new flexible photonic crystal designs