This talk will be about a series of works concerning the modeling of micro-magnetism for thin geometries. This presentation is the occasion to present the general properties of micro-magnetism physics and more specifically the phenomenons arising in small geometries and mainly the two case where the domain is a nano-particle (small sphere or small ellipse) or a nano-wire (cylinder or quasi-cylinder with small cross-section). In a second time I will present the contributions I made on these problems and models with P-A. Hervieux, G. Manfredi (physicists) and with R. Côte, C. Courtès, G. Ferrière, Y. Privat (mathematicians) in Strasbourg. The main focus of these works is the study of emergent meta-stable structures that are created on a short time-scale and their evolution in long time with or without external effects (temperature, external force,...). This include both theoretical analysis and numerical simulations.