Systems with competing energy scales are widespread and exhibit rich and subtle behaviour, although their systematic study is a relatively recent activity. This text presents lectures given at a NATO Advanced Study Institute reviewing the current knowledge and understanding of this fascinating subject, particularly with regard to phase transitions and dynamics, at an advanced tutorial level.
Both general and specific aspects are considered, with competitions having several origins; differences in intrinsic interactions, interplay between intrinsic and extrinsic effects, such as geometry and disorder; irreversibility and non-equilibration. Among the specific physical application areas are supercooled liquids and glasses, high-temperature superconductors, flux or vortex pinning and motion, charge density waves, domain growth and coarsening, and electron solidification.

Low temperature phases, ordering and dynamics in random media.- Statics and dynamics of the flux-line lattice in high-Tc superconductors.- Magnetic flux line lattices in the cuprate superconductors.- Theory and experiment of flux pinning and flux creep in high Tc superconductors.- Vortex line fluctuations in superconductors from elementary quantum mechanics.- Anisotropy and strong pinning in YBa2Cu3O7 with Y2BaCuO5 inclusions.- Interstitial and vacancy proliferation in flux line lattices.- Simulations of relaxation, pinning, and melting in flux lattices.- I-V characteristics of high temperature superconductors with correlated defects.- Relaxation near glass transition singularities.- Neutron scattering at the glass transition.- Susceptibilty studies of supercooled liquids and glasses.- Hierarchical melting of one-dimensionalincommensurate structures.- Charge density waves, phase slips, and instabilities.- Universality in commensurate-incommensurate phase transitions.- Glassy behaviour of the charge/spin density wave ground state.- The critical behavior of 1-d charge density waves.- Electron solidification in two dimensions.- Two-dimensional Wigner solid versus incompressible quantum liquid.- Domain growth and coarsening.- Critical wrinkling of depinned interfaces,strings and membranes.