Inertial electrostatic confinement (IEC) fusion is a technique by which electric fields confine and heat ions. The concept uses concentric electrodes to accelerate and focus ions thereby creating the conditions necessary for nuclear fusion. IEC cathodes may be mechanical, in the form of metallic grids or virtual, formed through trapping a net negative space charge. An experimental study was carried out into the operation of IEC devices of both types. The phenomenon of surface fusion in a gridded IEC was examined and the total fusion rate found to be dominated by atomic interactions on the cathode surface. The material and temperature of the IEC cathode were found to have a profound influence on the observed fusion rate, with graphite seen to perform exceptionally well when compared to transition metal cathodes. The research indicates that great improvements in the fusion efficiency of gridded IEC machines are possible through careful choice of grid material and the implementation of active cathode cooling. Also described is the design and construction, as well as initial operation of MCVC-0, a successor to previous Polywell style devices constructed at The University of Sydney. The device makes use of a biconic cusp magnetic field to confine electrons in space, thereby generating a virtual cathode. Biased and floating Langmuir probe measurements were used to examine potential well formation in the new machine, as well as diagnose the fundamental plasma parameters of temperature and density. Preliminary experimental work indicates poor performance of MCVC-0 with respect to virtual cathode formation and these shortcomings are addressed in terms of non-isotropic electrical conductivity in magnetised plasmas. The plasma conductivity model is extended to previously published virtual cathode machines and is shown to adequately describe the observed device behaviour, providing a possible alternate physical explanation for virtual cathode formation.