Stochastic kinetic models are used to describe a variety of biological, physical and chemical phenomena. One particularly interesting application is computational systems biology, where models are useful for contributing to the quantitative understanding of cellular processes through in{silico experimentation that would otherwise be difficult to undertake in a laboratory. Interest lies in statistical inference for the parameters which govern the dynamics of the system. Likelihood based inference is typically problematic, as discrete time transition kernels for models of this type are intractable in all but the most trivial systems. However, exact realisations can be drawn using a stochastic simulation algorithm. Techniques that rely only on the ability to forward simulate from the model, so called likelihood free inference methods, such as particle Markov chain Monte Carlo and approximate Bayesian computation (ABC) can be leveraged to infer system rate parameters. What is not clear however is how each technique behaves as the nature of the problem changes. This thesis explores the likelihood free methodology applied to stochastic kinetic models in a range of scenarios in order to draw comparisons between the various developments in each. A variety of models and data observation regimes on synthetic data are used to examine the effect of the choice of summary statistics and metrics on the inferred posterior distributions, prevalent questions within the ABC framework. Likelihood free techniques are considered computationally expensive hence it is necessary to consider the relative efficiency of the various approaches. The relative strengths and weaknesses of particle Markov chain Monte Carlo and approximate Bayesian computation are explored and utilised to develop a hybrid technique exploiting the stronger elements of each approach. The thesis concludes with inference of rate parameters for a logistic growth model applied to observations of a uorescent protein in different strains of the gram- positive bacterium, Bacillus subtilis.