We present a nonparametric mode-seeking algorithm, called medoidshift, based on approximating the local gradient using a weighted estimate of medoids. Like meanshift, medoidshift clustering automatically computes the number of clusters and the data does not have to be linearly separable. Unlike meanshift, the proposed algorithm does not require the definition of a mean. This property allows medoidshift to find modes even when only a distance measure between samples is defined. In this sense, the relationship between the medoidshift algorithm and the meanshift algorithm is similar to the relationship between the k-medoids and the k-means algorithms. We show that medoidshifts can also be used for incremental clustering of growing datasets by recycling previous computations. We present experimental results using medoidshift for image segmentation, incremental clustering for shot segmentation and clustering on nonlinearly separable data.