Much of the recent interest in semiconductor materials has focused on the ability to alter the composition and hence the band structure on the atomic scale, layer by layer. The quantum cascade laser is undoubtedly a tour de force in the understanding and application of semiconductor band structure engineering, demonstrating the growth control, physical understanding and engineering possibilities of advanced low-dimensional semiconductor structures. This chapter describes the possibility of extending semiconductor lasers across a broad new spectral range and into applications such as miniature radar, remote sensing, and laser-based pollution monitoring. Much elegant physics and many useful effects have been demonstrated in tunnelling structures, both for electronic and optoelectronic applications. The chapter reviews the principles of quantum mechanical tunnelling calculations, and describes briefly two of the most significant tunnelling devices. These tunnelling devices include double barrier resonant tunnelling devices, and quantum cascade laser structures.