Various resistive memory technologies are finding application in the space of storage-class memory and emerging non-von Neumann computing systems. For both applications, a key enabling technology is the ability to store multiple resistance levels in a single memory cell. The resistance states of these devices are typically measured in the low-field regime, where the electrical transport can be assumed to be Ohmic. However, when biased at slightly higher voltages, they exhibit significantly nonlinear I-V characteristics. In this paper, we demonstrate how this field dependence of the resistance values can be exploited in various applications. We present simulation and experimental results where readout schemes based on the non-linear I-V behavior are used to enhance the readout margin and also to compensate for resistance drift.