In recent years, many algorithms have been proposed to extract process models from process execution logs. The process models describe the ordering relationships between tasks in a process in terms of standard constructs like sequence, parallel, choice, and loop. Most algorithms assume that each trace in a log represents a correct execution sequence based on a model. In practice, logs are often noisy, and algorithms designed for correct logs are not able to handle noisy logs. In this paper we share our key insights from a study of noise in process logs both real and synthetic. We found that all process logs can be explained by a block‐structured model with two special self‐loop and optional structures, making it trivial to build a fully accurate process model for any given log, even one with inaccurate data or noise present in it. However, such a model suffers from low quality. By controlling the use of self‐loop and optional structures of tasks and blocks of tasks, we can balance the quality and accuracy trade‐off to derive high‐quality process models that explain a given percentage of traces in the log. Finally, new quality metrics and a novel quality‐based algorithm for model extraction from noisy logs are described. The results of the experiments with the algorithm on real and synthetic data are reported and analyzed at length.