Arumugam, GurusamyGurusamyArumugamTyagi, JagmohanJagmohanTyagi2025-08-312025-08-312021-02-0110.1007/s10440-020-00374-22-s2.0-85097526337https://d8.irins.org/handle/IITG2025/23755We recount and discuss some of the most important methods and blow-up criteria for analyzing solutions of Keller-Segel chemotaxis models. First, we discuss the results concerning the global existence, boundedness and blow-up of solutions to parabolic-elliptic type models. Thereafter we describe the global existence, boundedness and blow-up of solutions to parabolic-parabolic models. The numerical analysis of these models is still at a rather early stage only. We recollect quite a few of the known results on numerical methods also and direct the attention to a number of open problems in this domain.falseAsymptotic behavior of solutions | Blow-up | Boundedness | Chemotaxis | Discontinuous Galerkin method | Finite difference method | Finite element method | Finite Volume method | Global existence | Keller-Segel models | Local existence | Renormalized solutions | Stabilization | Weak solutionsArticle15729036February 20211066arJournal88WOS:000599931000005