Accurate and robust visual object tracking is one of the most challenging and fundamental computer vision problems. It entails estimating the trajectory of the target in an image sequence, given only its initial location, and segmentation, or its rough approximation in the form of a bounding box. Discriminative Correlation Filters (DCFs) and deep Siamese Networks (SNs) have emerged as dominating tracking paradigms, which have led to significant progress. Following the rapid evolution of visual object tracking in the last decade, this survey presents a systematic and thorough review of more than 90 DCFs and Siamese trackers, based on results in nine tracking benchmarks. First, we present the background theory of both the DCF and Siamese tracking core formulations. Then, we distinguish and comprehensively review the shared as well as specific open research challenges in both these tracking paradigms. Furthermore, we thoroughly analyze the performance of DCF and Siamese trackers on nine benchmarks, covering different experimental aspects of visual tracking: datasets, evaluation metrics, performance, and speed comparisons. We finish the survey by presenting recommendations and suggestions for distinguished open challenges based on our analysis. IEEE