  We provide a comprehensive overview and tooling for GP modeling with
non-Gaussian likelihoods using state space methods. The state space formulation
allows for solving one-dimensional GP models in $\mathcal{O}(n)$ time and
memory complexity. While existing literature has focused on the connection
between GP regression and state space methods, the computational primitives
allowing for inference using general likelihoods in combination with the
Laplace approximation (LA), variational Bayes (VB), and assumed density
filtering (ADF, a.k.a. single-sweep expectation propagation, EP) schemes has
been largely overlooked. We present means of combining the efficient
$\mathcal{O}(n)$ state space methodology with existing inference methods. We
extend existing methods, and provide unifying code implementing all approaches.
