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1. Projection matrices have become the dominant modelling approach in plant demography because they (i) are relatively easy to formulate, (ii) compile complex data in a structured and analytically tractable manner, (iii) provide numerous parameters with direct biological meaning, (iv) allow the investigator to address broad or specific, experimental and/or theoretical, ecological and evolutionary questions, and (v) produce uniform outputs, enabling direct comparisons between the results of different studies.2. The last decade has witnessed major advancements in this field that have brought demographic models much closer to the real world, in particular in the analysis of effects of spatial and temporal environmental variation on populations. The present Special Feature contributes to that progress with novel methodologies and applications on Integral Projection Models, stochastic Life Table Response Experiment analyses, stochastic elasticities, transient dynamics and phylogenetic analyses.3.Synthesis. Environmental stochasticity is an integral part of ecosystems, and plant populations exhibit a tremendous array of demographic strategies to deal with its effects. The analytical challenge of understanding how populations avoid, tolerate or depend on stochasticity is finally overcome with the new matrix approaches. The tools are now available to interpret the effects of changes in temporal and spatial variation on plant populations.