Robust model fitting essentially requires the application of two estimators. The first is an estimator for the values of the model parameters. The second is an estimator for the scale of the noise in the (inlier) data. Indeed, we propose two novel robust techniques: the two-step scale estimator (TSSE) and the adaptive scale sample consensus (ASSC) estimator. TSSE applies nonparametric density estimation and density gradient estimation techniques, to robustly estimate the scale of the inliers. The ASSC estimator combines random sample consensus (RANSAC) and TSSE, using a modified objective function that depends upon both the number of inliers and the corresponding scale. ASSC is very robust to discontinuous signals and data with multiple structures, being able to tolerate more than 80 percent outliers. The main advantage of ASSC over RANSAC is that prior knowledge about the scale of inliers is not needed. ASSC can simultaneously estimate the parameters of a model and the scale of the inliers belonging to that model. Experiments on synthetic data show that ASSC has better robustness to heavily corrupted data than least median squares (LMedS), residual consensus (RESC), and adaptive least Kth order squares (ALKS). We also apply ASSC to two fundamental computer vision tasks: range image segmentation and robust fundamental matrix estimation. Experiments show very promising results.