This thesis is concerned with the properties of two classes of exotic hadron: hy- brid mesons, in which an excitation of the gluonic field causes distinction from the conventional mesons and can give rise to J^PC quantum numbers not available to a qq̄ state; and pentaquarks, where the usual baryonic qqq structure is supplemented by a qq̄ pair, potentially giving the state an exotic flavour structure. In the hybrid meson sector, we work within the flux-tube model and extend upon an observation made by Isgur that the oscillations of the flux-tube can have dynamical effects upon the quarks living on the ends of the tube. We reverse the logic by allowing oscillations of the quarks caused by interactions with currents to excite modes in the flux-tube and hence hybrid mesons. Electromagnetic, weak and pionic currents are all applied, allowing us to make predictions about the radiative and hadronic decays of hybrid mesons and their production rates in exclusive hadronic decays of the B-meson. Such predictions are of interest to past, present and future experiments at E852, the B-factories and Jefferson Lab. In light of the possible observation of a pentaquark state, the Θ⁺ , we investigate some phenomenological consequences of certain models proposed to describe this state and attempt to justify one such model within a quark model framework. Jaffe and Wilczek's model for pentaquarks predicts in addition to the 10 [note: with a horizontal line above] with J^P=½ , a 10 [note: with a horizontal line above] with J^P=3/2⁺, the multiplets being initially degenerate. Within a dynamical model we are able to calculate the spin-orbit splitting between them and find it to not be large. We also consider the effect of a near degenerate 8 on the states in a pentaquark 10 [note: with a horizontal line above] , outlining a set of characteristic decay systematics that may be used in the search for non-flavour-exotic pentaquarks. In a constituent quark model with colour-spin interactions it is found to be possible to accommodate a Jaffe-Wilczek-like Θ⁺ with a rather low mass, while simultaneously describing the Δ-N splitting.