This thesis describes the investigation of a range of iron-based compounds which ex- hibit a variety of different electronic phases, from magnetoresistance to ferroelectricity. X-ray diffraction, neutron diffraction, and muon spectroscopy techniques were used to probe the magnetism to provide an explanation of the microscopic mechanism for the bulk electronic properties. X-ray diffraction is a set of techniques that probe electronic ordering in a periodic crystalline system. If the x-ray energy is tuned to an absorption edge of a magnetically active ion in the compound sensitivity to the magnetic order can be gained. These x-ray techniques were used to study magnetoresistance in SrFeO3−δ, revealing an interplay between the structural, charge and magnetic order as the origin. Neutron diffraction is an established set of techniques that can directly probe the magnetic order of a crystalline compound. Neutron diffraction was used in conjunction with x-rays to study the ferroelectric and Ising-like phases in the triangular lattice antiferromagnet CuFeO2, revealing strong spin-lattice coupling, the coexistence of antiferromagnetic and ferromagnetic phases and the splitting of the magnetic order in the ferroelectric phase into two inequivalent orbits with a phase separation between them. Diffraction techniques re- quire long-range order of the magnetic ground state to be of utility. Muon spectroscopy is a local probe that can study magnetism in systems where the magnetic order remains short-ranged. Muon spectroscopy was used to study the spin-freezing phenomena in Fe- CrAs, and revealed a two stage transition and interaction energies associated with them. Polarisation analysis was used together with resonant x-ray scattering to obtain quanti- tative information on the structure of the magnetic helical structure of FeAs, quantifying the degree of ellipticity to the magnetic helix, and revealing an out-of-plane oscillating canted structure to the spin helix
