This talk will provide an overview of computationally intensive methods for conducting Bayesian inference for the rate constants of stochastic kinetic intracellular reaction network models using single-cell time course data. Inference for the true Markov jump process is extremely challenging in realistic scenarios, so the true model will be replaced by a diffusion approximation, known in this context as the Chemical Langevin Equation (CLE). Inference for the CLE is also challenging, but the development of effective algorithms is possible, and turns out to be extremely effective, even in scenarios where one would expect the diffusion approximation to break down.