LED lamp has LEDs aimed rearwards with either a concave mirror to the rear of each LED, or one concave mirror to the rear of two or more LEDs, collecting the light from the LEDs to form a forward projecting beam. LEDs may be high power types that require heatsinking. LED lamp may have a lens forward of each LED to collimate the radiation produced by the LEDs into a beam, where at least one lens has at least one aspheric curved surface. LED lamp may have a transparent reflective optic to collimate the radiation produced by each LED into a beam. For an inspection lamp, the LEDs typically have a peak wavelength of 395 to 415 naometers for seeing the area being irradiated but not so visible as to overwhelm fluorescence of fluorescent materials to be detected. Other wavelengths may be used. LED inspection lamp has a combination of LEDs of different wavelengths or a combination of at least one LED and at least one other light source such that the lamp produces radiation suitable for detection of materials to be detected and adequately illuminates the area being irradiated. LED lamp has LEDs that produce a beam of suitable radiation with a width of 10 degrees or less without additional optics. LED inspection lamp has head attached to a flexible member, with head serving as heatsink for one or more high power LEDs. Current regulator circuits are also disclosed.