The present disclosure describes advanced lighting elements, in particular solid-state lighting elements, and luminaires that include an array of lighting elements. The lighting elements, and luminaires including the lighting elements can exhibit benefits that include high optical efficiency and therefore high luminous efficacy; extraordinary directional control and therefore extraordinary glare control and efficacy of delivered lumens; and exceptional mixing of individual-device emission providing exceptional suppression of punch-through and color breakup. In many cases, the architecture can be amenable to low-cost manufacturing in a modular format.