Theoretical aspects of multicomponent superconductivity and systemswith competing interactions are studied using Monte Carlo techniques.Motivated by recent experimental and theoretical results of complex struc-ture formation of vortices in multicomponent systems, possible vortex struc-ture formations due to vortex interactions that are not purely attractive orrepulsive are considered. Vortex structures such as clusters, superclusters,hierarchical structure formation, stripes, gossamer patters, glassy phases, aswell as checkerboard lattices and loops are demonstrated to be possible.The order of the superconducting phase transition is considered for multi-component lattice London superconductors. The phase transition is demon-strated to be either rst-order or continuous depending on the strength of asymmetry-breaking Josephson intercomponent interaction. It is argued thatthe rst-order phase transition is caused by a vortex phase separation due toa uctuation-induced attractive interaction between vortex lines. / <p>QC 20151117</p>