The aim of this thesis is to design the shape of nanocavities to tailor their radiated beam in terms of intensity and polarisation distribution, and emission direction. The radiative processes behind light amplification are revised, leading to the concept of laser device as a system composed of a gain medium, an optical cavity and a pump method. Next, the optoelectronic properties of semiconductor quantum wells and modal properties of whispering-gallery mode cavities are described, justifying why they were chosen as gain medium and optical cavity for the nanolasers studied in this thesis. We engineered the cavity shape of the nanolasers with an automated inverse design method based on topology optimisation, which demonstrated to yield photonic devices with novel geometries that outperform those designed by conventional means, such as parametric sweeps, based on the intuition of the user. We prove the generality of this inverse method by designing and experimentally verifying nanolasers that produce three different beams: a gaussian-like beam with linear polarisation, and two doughnut beams with azimuthal and radial polarisation. The nanolasers are fabricated via electron-beam lithography and etching processes. The output laser beams are characterised by Fourier microscopy and k-space polarimetry, to analyse their intensity and polarisation angular distribution, and yield overlaps of up to 92%, 96% and 85% with the target modes for the azimuthal, radial and linearly polarised cases, respectively. The lasing performance of the nanolasers is studied by fitting the input power output power curve to a laser model and is compared to the literature. More power is collected from the inverse-designed nanolasers thanks to their axial emission, compared to conventional circular microdisc lasers. In summary, in this thesis we demonstrate the validity of the inverse design method in the engineering of ultra-compact lasers with tailored beams.Engineering and Physical Sciences Research Council (EPSRC)