The utility of unit cell models that assume periodic microstructures may be limited when applied to cellular materials that have non-periodic microstructures. We analyzed the effects of non-periodic microstructure and defects on the compressive failure behavior of Voronoi honeycombs using finite element analysis. Our results indicate that the non-periodic arrangement of cell walls in random Voronoi honeycombs (with cells approximately uniform in size) results in higher strains in a small number of cell walls compared to periodic, hexagonal honeycombs. Consequently, the Voronoi honeycombs were approximately 30% weaker than periodic, hexagonal honeycombs of the same density. The strength difference between the Voronoi and periodic honeycombs depended slightly on density, due to density-dependent interactions between failure modes (i.e. plastic collapse and elastic buckling). Defects, introduced by removing cell walls at random locations, caused a sharp decrease in the effective mechanical properties of both Voronoi and periodic honeycombs (e.g. a 10% reduction in density due to defects caused a 60% reduction in the strength of Voronoi honeycombs). The sensitivity to defects was comparable for thin-walled, elastomeric honeycombs (relative density 0.015) and for thicker walled, plastic honeycombs (relative density 0.15). The properties degraded to zero when 35% of the cell walls were removed, consistent with the percolation limit for a two-dimensional network of hexagonal cells. When four or more adjacent cell walls were removed, the localized band of cell collapse passed through the defect site and the effective strength and modulus were reduced, indicating that even those defects which have a negligible effect on density can alter the failure pattern as well as the effective properties of honeycombs with cells of approximately equal size and strength.