There once was a harsh competition between different computer memory technologies, and now we cheer triumph for the Random Access-Memory (RAM) devices, -- cheap, fast, tiny, stable. The competing Magnetic Bubble Memory had faded away as magnetic bubbles are undesirably large and pretty much not robust, manifesting both low data density and high operational costs. However, what we do possess now are nanosize objects of topological nature, magnetic skyrmions, which are protected from continuous field variations and take very little energy cost to be moved. Thus, skyrmions are considered as promising information carriers for future memory devices and ultradense data storage, while skyrmion phases in bulk materials are interesting from fundamental point of view in exploring topological states of matter. In this thesis, I develop and advance several effective theoretical approaches, diverse both in their methods and use, which were of appeal for several skyrmionic experiments in our lab (LQM/EPFL). We were and are primarily interested in the open issues in the applied field of skyrmionics, which may be taken under the umbrella of creation, stabilization and control of magnetic skyrmions under electric fields, mechanical strains, thermal gradients, etc. For the goals achieved and yet to be achieved, the magnetoelectric insulator Cu2OSeO3, which uniquely responses to all the above mentioned fields, is a highly advantageous candidate. Magnetoelectric here means that the spins of a magnetic material are coupled to external electric fields, while insulating properties are very advantageous to preserve both the state and the very existence of skyrmions by eliminating the Joule heating. The novel results in this thesis are calculations for both individual and arrayed skyrmions under electric fields, mechanical strains and uniform pressures, and thermal gradients. Furthermore, several fundamental questions were addressed by developing an extended formalism for calculation skyrmion-pocket phase diagrams, studying the topologically-governed crossover between skyrmions and magnetic bubbles, and discussing the possible role of merons (half-skyrmions) in skyrmion phase formation. The result with the most immediate appeal is probably the theoretical and experimental study of skyrmion lattices in electric fields, with a direct demonstration of writing and erasing of the full skyrmion phase under electric fields of few Volts per micrometer, as compatible with modern microelectronic devices.