This thesis introduces and explores the full global interplanetary trajectory optimisation problem. The biggest challenges in this field are expensive objective function evaluations, the size and multimodality of the search space, a requirement for good initial solutions to initialise search algorithms, the need for manual input and separate solutions to solve the combinatorial and continuous elements of the problem and finally solution robustness. The literature is summarised, analysing current solution methods, global algorithms, software and toolboxes with respect to the challenges identified. It is concluded that Monte Carlo Tree Search and hybrid evolutionary algorithms are perhaps the most effective algorithms currently in use. Though techniques used for search space reduction and approximation (that are algorithm agnostic) can have just as large an impact. Opportunities for further work into algorithm parameter optimisation, machine learning for search space reduction and extended objective function approximation are outlined.