Linear structural models are linear relationships between two stochastic (random) variates in which both of the variates are subject to measurement errors. Structural models are common in experimental work, but are typically fit using least squares. In this expository paper maximum likelihood estimators for linear structural models are presented and contrasted with the corresponding least squares estimators. Asymptotic variance formulae for the intercept and slope estimators are given, along with the corresponding expressions for linear functional models.