The paper discusses the standard approaches in constructing the spatial weights matrix, W, and the implications of using such approaches in terms of the potential mis-specification of W. We then look at more recent attempts to measure W in the literature, including: Bayesian (searching for 'best fit'); non-parametric techniques; the use of spatial correlation to estimate W; other iteration techniques; and alternative approaches. Lastly, an illustration is provided based on estimating spatial lag models determining establishment level R&D spending in the UK, finding that differently constructed W matrices produce different estimates of spatial spillovers.