LTS_LINEFIT and LTS_PLANEFIT are IDL programs to robustly fit lines and planes to data with intrinsic scatter. The code combines the Least Trimmed Squares (LTS) robust technique, proposed by Rousseeuw (1984) and optimized in Rousseeuw & Driessen (2006), into a least-squares fitting algorithm which allows for intrinsic scatter. This method makes the fit converge to the correct solution even in the presence of a large number of catastrophic outliers, where the much simpler σ-clipping approach can converge to the wrong solution. The code is also available in Python as ltsfit.