2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/108915This is a survey of the recent work in algorithmic and asymptotic properties of groups. I discuss Dehn functions of groups, complexity of the word problem, Higman embeddings, and constructions of finitely presented groups with extreme properties (monsters).To appear in the Proceedings of ICM in Madrid, 22 pagesGroup TheoryGeometric Topologytext