Thermal rectification, or the asymmetric transport of heat along a structure, has recently been investigated as a potential solution to the thermal management issues that accompany the miniaturization of electronic devices. Applications of this concept in thermal logic circuits analogous to existing electronics-based processor logic have also been proposed. This review highlights some of the techniques that have been recently investigated for their potential to induce asymmetric thermal conductivity in solid-state structures that are composed of materials of interest to the electronics industry. These rectification approaches are compared in terms of their quantitative performance, as well as the range of practical applications that they would be best suited to. Techniques applicable to a range of length scales, from the continuum regime to quantum dots, are discussed, and where available, experimental findings that build upon numerical simulations or analytical predictions are also highlighted.