Light engine modules including a support member and a solid state light emitter, in which (1) the emitter is mounted on the support member, (2) a region of the support member has a surface with a curved cross-section, (3) the emitter and a compensation circuit are mounted on the support member, (4) an electrical contact element extends to at least two surfaces of the support member, and/or (5) a substantial entirety of the module is located on one side of a plane and the emitter emits light into another side of the plane. Also, a module in which a light emitter is supported. Also, a lighting device including a housing member and a light emitter mounted on a removable support member. Also, a lighting device including a module mounted in a lighting device element. Also, a method including mounting a module to a lighting device element.