Methods of operating a ferroelectric memory cell. The method includes applying one of a positive bias voltage and a negative bias voltage to a ferroelectric memory cell having a capacitor including a top electrode, a bottom electrode, a ferroelectric material between the top electrode and the bottom electrode, and an interfacial material between the ferroelectric material and one of the top electrode and the bottom electrode. Another of the positive bias voltage and the negative bias voltage is applied to the ferroelectric memory cell to switch a polarization of the ferroelectric memory cell, wherein an absolute value of the negative bias voltage is different from an absolute value of the positive bias voltage. Related ferroelectric memory cells include a ferroelectric material exhibiting asymmetric switching properties.