Bayesian optimisation (BO) has been increasingly utilised to guide material discovery. While BO is advantageous due to its sample efficiency, flexibility and versatility, it is constrained by a range of core issues including high-dimensional optimisation, mixed search space, multi-objective optimisation and multi-fidelity data. Although various studies have attempted to tackle one or some challenges, a comprehensive BO framework for material discovery is yet to be uncovered. This work provides a short review aiming at connecting algorithmic advancement to material applications. Open algorithmic challenges are discussed and supported by recent material applications. Various open-source packages are compared to assist the selection. Furthermore, three exemplary material design problems are analysed to demonstrate how BO could be useful. The review concludes with an outlook on BO-aided autonomous laboratory.