This paper surveys locally weighted learning, a form of lazy learning and memory-based learning, and focuses on locally weighted linear regression. The survey discusses distance functions, smoothing parameters, weighting functions, local model structures, regularization of the estimates and bias, assessing predictions, handling noisy data and outliers, improving the quality of predictions by tuning fit parameters, interference between old and new data, implementing locally weighted learning efficiently, and applications of locally weighted learning. A companion paper surveys how locally weighted learning can be used in robot learning and control.