As current CMOS based technologies are approaching their anticipated limits, emerging nanotechnologies start to replace their role in electronic circuits. New computing models have been proposed. This chapter overviews both deterministic and stochastic computing models targeting nano-crossbar switching arrays and emerging low-density circuits. These models are demonstrated with implementations using Boolean and arithmetic logic. Performance parameters of the models such as area, speed, and accuracy, are also evaluated in comparison with those of conventional circuits.