Advanced optical design methods using the tools of nonimaging optics (instead of conventional imaging tools) produce ultracompact devices that combine high collection efficiency with a concentration (or collimating) capability close to the thermodynamic limit. After a general overview covering the most important design methods and devices in nonimaging optics, two of these designs, the so-called RX and RXI, are presented. Even though it is designed within the nonimaging framework, the RX device nevertheless has imaging properties that complement its valuable performance as a nonimaging device. The RXI is extremely compact: its aspect ratio (thickness/aperture diameter) is less than 1/3. When working as a receiver, that is, by placing a photodiode in the correct position, it attains an increase in irradiance that takes it beyond 95% of the theoretical thermodynamic limit (i.e., a concentration of 1600 times with an acceptance angle of ±2.14 deg). As an emitter, similar intensity gains can be obtained within an angle almost as large as 95% of the thermodynamic limit. The combination of high concentration factors, relatively wide acceptance angles, simplicity, and compactness makes these devices almost unique. The measurements carried out with several RXI prototypes, all of them made by PMMA injection, are also presented.