This thesis presents experimental studies of the electronic and magnetic properties of several iron-based unconventional superconductors, primarily using the techniques of magnetotransport and torque magnetometry in high magnetic fields and synchrotron-based angle-resolved photo-emission spectroscopy (ARPES). Superconductivity in the iron-based superconductors is always found in proximity to a magnetic phase, and the details of the electronic structure and Fermi surface are also important in determining the strength of interactions, and ultimately superconductivity. This motivates the experimental studies of electronic, magnetic and superconducting properties of Fe-based superconductors presented in this thesis. First, quantum oscillation measurements using high-field torque magnetometry are used to provide a partial determination of the Fermi surface of superconducting LiFeAs. The data are compared with density functional theory calculations, finding strong mass enhancements on the observed electron bands, however the hole bands are not observed. A large portion of this thesis concerns experiments on FeSe, which uniquely has a structural transition but is not magnetically ordered at any temperature. High field magnetotransport measurements show quantum oscillations, revealing small quasi-two dimensional Fermi surfaces, and it is argued that both hole and electron pockets are observed. The low-temperature Fermi surface consisting of one hole pocket and two electron pockets is also deduced from low-field magnetotransport. ARPES studies show that both hole and electron pockets undergo a significant elongation when cooling through the structural transition at ~90 K, interpreted as the result of orbital order. Measurements of the resistivity anisotropy above the structural transition are used to show that the structural distortion is electronically-driven. By combining these data sets, a complete picture of the symmetry-broken electronic structure of FeSe is constructed. The final chapter concerns another iron-based superconductor with a more complex crystal structure, the so-called ``10-3-8" phase, and in particular finds an unusual field-induced magnetic transition.