This work is the concatenation of three papers, all revolving around Bayesian statistics. The first one concerns Bayesian phylogenetical inference with application to historical linguistics of Sign Languages. We develop a model for matricial datasets where lines and columns evolves jointly, this can represent vocabulary datasets or even socio-cultural traits. We are able to compute the likelihood associated with this model, and to sample from the posterior by using Sequential Monte Carlo methods with exotic tempering. The results on simulated datasets are quite satisfactory and the results on real dataset confronts the hypothesis of the linguists.The second deals with approximate Bayesian computation. These methods are useful for generative models with intractable likelihoods. These methods are however sensitive to the dimension of the parameter space, requiring exponentially increasing resources as this dimension grows. To tackle this difficulty, we explore a Gibbs version of the ABC approach that runs component-wise approximate Bayesian computation steps aimed at the corresponding conditional posterior distributions, and based on summary statistics of reduced dimensions. While lacking the standard justifications for the Gibbs sampler, the resulting Markov chain is shown to converge in distribution under some partial independence conditions. The associated stationary distribution can further be shown to be close to the true posterior distribution and some hierarchical versions of the proposed mechanism enjoy a closed form limiting distribution. Experiments also demonstrate the gain in efficiency brought by the Gibbs version over the standard solution.The third is dedicated to interacting particle methods. Over the last decades, various "non-linear" MCMC methods have arisen. While appealing for their convergence speed and efficiency, their practical implementation and theoretical study remain challenging. We introduce a large class of non-linear samplers that can be studied and simulated as the mean-field limit of a system of interacting particles. The practical implementation we propose leverages the computational power of modern hardware (GPU).