Utilizing meta-heuristic global optimization algorithms in gas turbine aero-engines modelling and control problems is proposed over the past two decades as a methodological approach. The purpose of the review is to establish evident shortcomings of these approaches and to identify the remaining research challenges. These challenges need to be addressed to enable the novel, cost-effective techniques to be adopted by aero-engine designers. First, the benefits of global optimization algorithms are stated in terms of philosophy and the nature of different types of these methods. Then, a historical coverage is given for the applications of different optimization techniques applied in different aspects of gas turbine modelling, controller design, and tuning fields. The main challenges for the application of meta-heuristic global optimization algorithms in new advanced engine designs are presented. To deal with these challenges, two efficient optimization algorithms, Competent Genetic Algorithm in single objective feature and aggregative gradient-based algorithm in multi-objective feature are proposed and applied in a turbojet engine controller gain-tuning problem as a case study. A comparison with the publicly available results show that optimization time and convergence indices will be enhanced noticeably. Based on this comparison and analysis, the potential solutions for the remaining research challenges for application to aerospace engineering problems in the future include the implementation of enhanced and modified optimization algorithms and hybrid optimization algorithms in order to achieve optimal results for the advanced engine modelling and controller design procedure with affordable computational effort.