In the past five years biotechnological innovations have enabled the measurement of transcriptome-wide gene expression in single-cells. However, the destructive nature of the measurement process precludes genuine time-series analysis of e.g. differentiating cells. This has led to the pseudotime estimation (or cell ordering) problem: given static gene expression measurements alone, can we (approximately) infer the developmental progression (or "pseudotime") of each cell? In this talk I will introduce the problem from the typical perspective of manifold learning before re-casting it as a (Bayesian) latent variable problem. I will discuss approaches including nonlinear factor analysis and Gaussian Process Latent Variable Models, before introducing a new class of covariate-adjusted latent variable models that can infer such pseudotimes in the presence of heterogeneous environmental and genetic backgrounds.