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Periodic arrays of resonant dielectric nano- or microstructures provide perfect reflection across spectral bands whose extent is controllable by design. At resonance, the array yields this result even in a single subwavelength layer fashioned as a membrane or residing on a substrate. The resonance effect, known as guided-mode resonance, is basic to modulated films that are periodic in one dimension (1D) or in two dimensions (2D). It has been known for 40 years that these remarkable effects arise as incident light couples to leaky Bloch-type waveguide modes that propagate laterally while radiating energy. Perfect reflection by periodic lattices derives from the particle assembly and not from constituent particle resonance. We show that perfect reflection is independent of lattice particle shape in the sense that it arises for all particle shapes. The resonance wavelength of the Bloch-mode-mediated zero-order reflectance is primarily controlled by the period for a given lattice. This is because the period has direct, dominant impact on the homogenized effective-medium refractive index of the lattice that controls the effective mode index experienced by the mode generating the resonance. In recent years, the field of metamaterials has blossomed with a flood of attendant publications. A significant fraction of this output is focused on reflectors with claims that local Fabry-Perot or Mie resonance causes perfect reflection with the leaky Bloch-mode viewpoint ignored. In this paper, we advance key points showing the essentiality of lateral leaky Bloch modes while laying bare the shortcomings of the local mode explanations. The state of attendant technology with related applications is summarized. The take-home message is that it is the assembly of particles that delivers all the important effects including perfect reflection.