Memristors have shown an extraordinary potential to emulate the plastic and dynamic electrical behaviors of biological synapses and have been already used to construct neuromorphic systems with in-memory computing and unsupervised learning capabilities; moreover, the small size and simple fabrication process of memristors make them ideal candidates for ultradense configurations. So far, the properties of memristive electronic synapses (i.e., potentiation/depression, relaxation, linearity) have been extensively analyzed by several groups. However, the dynamics of electroforming in memristive devices, which defines the position, size, shape, and chemical composition of the conductive nanofilaments across the device, has not been analyzed in depth. By applying ramped voltage stress (RVS), constant voltage stress (CVS), and pulsed voltage stress (PVS), we found that electroforming is highly affected by the biasing methods applied. We also found that the technique used to deposit the oxide, the chemical composition of the adjacent metal electrodes, and the polarity of the electrical stimuli applied have important effects on the dynamics of the electroforming process and in subsequent post-electroforming bipolar resistive switching. This work should be of interest to designers of memristive neuromorphic systems and could open the door for the implementation of new bioinspired functionalities into memristive neuromorphic systems.