Efficient methods for Bayesian inference of state space models via Markov chain Monte Carlo (MCMC) based on parallel importance sampling type weighted estimators (Vihola, Helske, and Franks, 2020, <doi:10.1111/sjos.12492>), particle MCMC, and its delayed acceptance version. Gaussian, Poisson, binomial, negative binomial, and Gamma observation densities and basic stochastic volatility models with linear-Gaussian state dynamics, as well as general non-linear Gaussian models and discretised diffusion models are supported. See Helske and Vihola (2021, <doi:10.32614/RJ-2021-103>) for details.