Abstract: In this thesis we investigate the emergence of new phenomena in multigap superconductors and multicomponent Ginzburg-Landau theories in the presence of intraband and cross-band pairing. The first part contains a review of emergent phenomena in superconductors with only intraband pairing, in particular the mechanism behind gap resonances which are accompanied by Higgs and Leggett modes. Then we study the gap resonances induced by two-dimensional quantum confinement and describe its spatial profile using the Bogoliubov-de Gennes equations. In the second part we describe the conditions where the cross-band pair formation is feasible. Using the formalism of Green functions we obtain the equations governing the interplay between intraband and cross-band pairing. Also, we derived the Ginzburg-Landau equations considering both intraband and cross-band pairing. Finally, we describe the crossover between the intraband-dominated and crossband-dominated regimes. These two are delimited by a tendency towards a gapless state. When a magnetic field is applied close to the gapless state, we found new arrangements of vortices like square lattices, stripes, labyrinths or of vortex clusters. The experimental signatures and consequences of crosspairing are discussed for MgB2 and Ba0.6K0.4Fe2As2.