This paper presents the results of SHREC'21 track: Quantifying Shape Complexity. Our goal is to investigate how good the submitted shape complexity measures are (i.e. with respect to ground truth) and investigate the relationships between these complexity measures (i.e. with respect to correlations). The dataset consists of three collections: 1800 perturbed cube and sphere models classified into 4 categories, 50 shapes inspired from the fields of architecture and design classified into 2 categories, and the data from the Princeton Segmentation Benchmark, which consists of 19 natural object categories. We evaluate the performances of the methods by computing Kendall rank correlation coefficients both between the orders produced by each complexity measure and the ground truth and between the pair of orders produced by each pair of complexity measures. Our work, being a quantitative and reproducible analysis with justified ground truths, presents an improved means and methodology for the evaluation of shape complexity. (C) 2021 Elsevier Ltd. All rights reserved.