In this short course I will overview estimation and inference in regression models of increasing parameter dimension, meaning that the parameter dimension K grows with the sample size N. In the first part, I will discuss basic and new results on least squares, quantile regression processes, generalized method-of-moments, and Bayes-type estimators under the condition that K/N tends to zero, including functional central limit theorems, strong approximations, and uniform inference. I will illustrate these results with econometric applications, such as inference on intersections bounds, inference under shape constraints, and instrumental regression. In the second part, I will discuss basic and new results on L1 penalized least squares, quantile regression processes, and m-estimators under the condition that K/N tends to infinity. I will illustrate these results with econometric applications, including instrument selection and growth regressions.