Today magnets form part of our daily life. They are responsible for most of the energy generation (e.g. turbines), conversion (e.g. transformers) and its use (e.g. motors). In these applications the precise control of magnetic fields and magnetization is essential to devise new applications or to improve the existing ones. All these would not be possible without an impressive development of magnetic materials. For example, in the last century very large (hard magnets) and very small (soft magnets) values of crystalline anisotropy have been achieved, spanning in five orders of magnitude. The vast range of coercivities makes possible the design of the shape of the hysteresis loop desired for a particular application. Soft ferromagnets are of great interest because they can guide and concentrate magnetic fields and present low hysteresis and large values of both saturation magnetization and susceptibility. These materials are found, for instance, in electromagnets, where a soft ferromagnetic core is set to concentrate the field, and in electrical transformers, motors or generators, in which the low power loss is an advantage. The large number of existing and potential applications of soft ferromagnets ranges from large scales (meters) to very small scales (nanometers). One of the large scale applications is superconducting magnetic levitation. Superconductors have demonstrated to present stable and passive levitation lifting weights of hundreds of kilograms. Using these concepts, superconducting materials can be located in a vehicle that levitates above a permanent-magnet guideway in what is known a magnetic levitation vehicle. The main advantage of this technology is its contactless nature which allows a major reduction of friction, and therefore larger vehicle speeds can be achieved with the same power consumption. Soft ferromagnets located in the guideway modify the magnetic field landscape of the permanent magnets leading to optimized values of levitation force and stability of the levitating superconducting vehicle. At the small scale, a very important application of soft ferromagnets is in magnetic recording and since few decades ago, this industry has been pushing hard in the deep understanding of magnetism at the nanoscale. In essence magnets produce magnetic fields that can be used to store bits of information. This information can be read using a magnetoresistive read head that consists of a multilayer of soft ferromagnetic-metal-soft ferromagnetic with one of the ferromagnetic layers (pinned layer) attached to an antiferromagnet. The other ferromagnetic layer is free to sense the magnetic field at very small spatial scales. Information can also be stored in arrays of magnetic tunnel junctions or simply cylindrical soft ferromagnets. These latter ones can present a magnetic vortex state at remanence, a magnetization pattern that can store two bits of information increasing the information density (number of bits per area of magnetic media). The aim of the present thesis is to model the behavior of soft ferromagnets in the macroscopic and microscopic scales and their interaction with other magnetic materials such as permanent magnets, superconductors or antiferromagnets for their use in the mentioned applications. This thesis is structured in two parts. In Part I we introduce a model that describes the mutual interaction of a linear, isotropic, and homogeneous soft ferromagnetic bar with a hard type II superconductor. The model is applied to the optimization of a typical magnetic levitation guideway. In Part II a non linear model based on micromagnetic scheme is introduced to model soft ferromagnets at the nanoscale range. The model is applied to the study of exchange biased systems and the control of magnetic vortex states.