Bayesian inference on complex models is challenging, as long simulation times and large observational data sets can make computation infeasible and posterior samplers can struggle with high-dimensional parameter spaces with complex posterior geometries. However, several active areas of research offer methods to address some of these challenges, such as Hamiltonian Monte Carlo (HMC) to use gradient information for robust posterior sampling, Stochastic Variational Inference (SVI) for faster inference which is robust to noisy data, Neural Networks (NNs) and Neural Density Estimators (NDEs) for fast and scalable approximations of deterministic functions and stochastic processes. However, they are yet to find adoption for the more complex, realistic, long running models in the sciences, such as climate, astrological or disease transmission models. Fast and scalable inference for these models would result in timely scientific understanding and policy making which could have a far-reaching impact on our societies. Newer methods of inference are of particular interest in global malaria research, where models have grown in complexity. These often include hundreds of parameters which influence an intricate combination of non-linear dynamics, need to be fit to several decades of global prevalence and incidence data, and simulations for each location take many hours to execute. Researchers have developed these models to meet the growing demands for malaria control and elimination in a widening landscape of potential interventions and confounding dynamics-such as new vaccines, insecticide resistance and a changing climate. Bayesian inference of model parameters affects the predictive power of malaria transmission forecasts when estimating burden or planning intervention strategies, which impacts hundreds of millions of lives globally. New methods are needed to ensure that researchers can perform inference on malaria transmission models as they grow to capture the nuances of modern malaria. This thesis documents my investigations into new methods which could address these needs.