The two-volume set LNAI 13067 and 13068 constitutes the proceedings of the 20th Mexican International Conference on Artificial Intelligence, MICAI 2021, held in Mexico City, Mexico, in October 2021. The total of 58 papers presented in these two volumes was carefully reviewed and selected from  129 submissions. The first volume, Advances in Computational Intelligence, contains 30 papers structured into three sections: - Machine and Deep Learning - Image Processing and Pattern Recognition - Evolutionary and Metaheuristic Algorithms The second volume, Advances in Soft Computing, contains 28 papers structured into two sections: - Natural Language Processing - Intelligent Applications and Robotics