Plant breeding trials aim to identify new varieties or breeding lines with enhanced traits (e.g. yield) for use as parents or for commercial release. The identification is generally based on data from a designed experiment, often conducted on a number of fields across location and/or years collectively referred to as multi-environmental field trial (MET) data. The analysis of MET data motivates various statistical models to obtain accurate genotype-by-environment (GxE) effects. I will explain the motivation behind the different statistical models with particular emphasis on the use of factor analytic (FA) models. FA models are particularly attractive due to computational advantages and potential interpretation of the factor loading. Pertinent to FA models is the order selection and I will introduce our recent development in this (Hui, Tanaka & Warton, 2018 published in Biometrics). The talk will aim to be pedagogical and illustrate concepts with examples.