This thesis treats interaction between electromagnetic waves and localized plasma oscillations. Two specific physical systems are considered, namely artificially excited magnetic field-aligned irregularities (striations) and naturally excited lower hybrid solitary structures (LHSS). Striations are mainly density depletions of a few percent that are observed when a powerful electromagnetic wave, a pump wave, is launched into the ionosphere. The striations are formed by upper hybrid (UH) oscillations that are localized in the depletion where they are generated by the linear conversion of the pump field on the density gradients. However, the localization is not complete as the UH oscillation can convert to a propagating electromagnetic Z mode wave. This process, termed Z mode leakage, causes damping of the localized UH oscillation. The Z mode leakage is investigated and the theory predicts non-Lorentzian skewed shapes of the resonances for the emitted Z mode radiation. Further, the interaction between individual striations facilitated by the Z mode leakage is investigated. The LHSS are observed by spacecraft in the ionosphere and magnetosphere as localized waves in the lower hybrid (LH) frequency range that coincides with density cavities. The localized waves are immersed in non-localized wave activity. The excitation of localized waves with frequencies below LH frequency is modelled by scattering of electromagnetic magnetosonic (MS) waves off a preexisting density cavity. It is shown analytically that an incident MS wave with frequency less than the minimum LH frequency inside the cavity is focused to localized waves with left-handed rotating wave front. In addition, the theory is shown to be consistent with observations by the Freja satellite. For frequencies between the minimum LH frequency inside the cavity and the ambient LH frequency, the MS wave is instead mode converted and excites pressure driven LH oscillations. This process is studied in a simplified geometry.