Most plant breeding trials involve a layout of plots in rows and columns. Resolvable row-column designs have proven effective in obtaining efficient estimates of treatment effects. Further improvement may be possible by postblocking or by inclusion of spatial model components. This study reviews options for augmenting a baseline row-column model by the addition of spatial components. The models considered are different variants of the linear variance model in one and two dimensions. Usefulness of these options is assessed by analysing a number of field trials from plant breeding and variety testing.Key words: field trial -linear variance -residual maximum likelihood -resolvable row-column designs -separabilityspatial analysis Spatial modelling of field trials has received considerable attention in the past (Wilkinson et al. 1983, Green et al. 1985, Besag and Kempton 1986, Kempton et al. 1994, Besag and Higdon 1999, Watson 2000, Edmondson 2005, McCullagh and Clifford 2006, Campbell and Bauer 2007, Piepho et al. 2008, and with the advent of powerful statistical packages, fullyfledged REML-based mixed model analyses with spatial covariance structures can conveniently be used for crop variety trials and plant breeding trials (Smith et al. 2005).A large number of spatial models have been proposed for field trial data, so spatial analysis requires a number of choices to be made. Thus, model selection and precautions against overfitting become a major issue. The danger of over-fitting increases with the number of candidate models being tried on the data, so it is advisable to limit the number of model choices at the design stage. In some applications of spatial modelling for field trials, spatial models have been treated as alternatives to the use of blocking and classical design principles. Recently, interest has increased in finding optimal designs with a particular spatial analysis in mind (Cullis et al. 2006, Martin et al. 2006, Butler et al. 2008. Taking a somewhat intermediate stance, Williams et al. (2006) proposed resolvable spatial row-column designs based on linear variance (LV) models, which provide randomization protection via the option of reverting to classical analysis for row-column designs when the spatial component does not lead to an improved fit. Thus, analysis may proceed by fitting a baseline model with row and column effects and checking if addition of a spatial component is worthwhile. This approach, while allowing spatial correlation to be exploited, uses only a very limited set of candidate models. Also, users of a spatial rowcolumn design are protected if a particular data set demands a complex variance-covariance structure while paying only a small premium in reduced precision if several of the spatial variance-covariance parameters turn out to be relatively small.This study describes two-dimensional LV models for resolvable row-column designs. It investigates the model proposed by Williams et al. (2006) and proposes a new model, which meets the separability condition (Martin 1979). ...