Abstract Finlay–Wilkinson regression is a popular method for analysing genotype–environment interaction in series of plant breeding and variety trials. It involves a regression on the environmental mean, indexing the productivity of an environment, which is driven by a wide array of environmental factors. Increasingly, it is becoming feasible to characterize environments explicitly using observable environmental covariates. Hence, there is mounting interest to replace the environmental index with an explicit regression on such observable environmental covariates. This paper reviews the development of such methods. The focus is on parsimonious models that allow replacing the environmental index by regression on synthetic environmental covariates formed as linear combinations of a larger number of observable environmental covariates. Two new methods are proposed for obtaining such synthetic covariates, which may be integrated into genotype‐specific regression models, that is, criss‐cross regression and a factor‐analytic approach. The main advantage of such explicit modelling is that predictions can be made also for new environments where trials have not been conducted. A published dataset is employed to illustrate the proposed methods.