Chemotaxis and cross-diffusion models in complex environments: Models and analytic problems toward a multiscale vision Bellomo, Nicola Soler Vizcaino, Juan Segundo Keller–Segel Cross diffusion Multiscale problems Pattern formation Complex interactions Blow-up Well-posedness Micro-macro derivation Juan Soler and Nicola Bellomo acknowledge the support by the MINECO-Feder (Spain) research Grant Number RTI2018-098850-B-I00, the Junta de Andalucia (Spain) Project PY18-RT-2422, A-FQM-311-UGR18 & B-FQM-580-UGR20. Youshan Tao is partially supported by the National Natural Science Foundation of China (No. 12171316), and he also acknowledges support of Shanghai Frontiers Science Center of Modern Analysis. MichaelWinkler acknowledges support of the Deutsche Forschungsgemeinschaft in the context of the Project Emergence of Structures and Advantages in CrossDiffusion Systems (No. 411007140, GZ: WI 3707/5-1). This paper proposes a review focused on exotic chemotaxis and cross-diffusion models in complex environments. The term exotic is used to denote the dynamics of models interacting with a time-evolving external system and, specifically, models derived with the aim of describing the dynamics of living systems. The presentation first, considers the derivation of phenomenological models of chemotaxis and cross-diffusion models with particular attention on nonlinear characteristics. Then, a variety of exotic models is presented with some hints toward the derivation of new models, by accounting for a critical analysis looking ahead to perspectives. The second part of the paper is devoted to a survey of analytical problems concerning the application of models to the study of real world dynamics. Finally, the focus shifts to research perspectives within the framework of a multiscale vision, where different paths are examined to move from the dynamics at the microscopic scale to collective behaviors at the macroscopic scale. 2022-06-02T10:43:04Z 2022-06-02T10:43:04Z 2022-04-18 journal article Bellomo, N... [et al.] (2022). Chemotaxis and cross-diffusion models in complex environments: Models and analytic problems toward a multiscale vision. Mathematical Models and Methods in Applied Sciences, 32(04), 713-792. DOI: [10.1142/S0218202522500166] http://hdl.handle.net/10481/75199 10.1142/S0218202522500166 eng http://creativecommons.org/licenses/by/3.0/es/ open access Atribución 3.0 España World Scientific