ITRS has identified nano-magnet based spintronic devices as promising post-CMOS technologies for information processing and data storage due to their ultra-low switching energy, non-volatility, superior endurance, excellent retention time, high integration density and compatibility with CMOS technology. As for data storage, spintronic memory has been widely accepted as a universal high performance next-generation non-volatile memory candidate. As for information processing, spintronic computing remains complementary in its features to CMOS technology. In this paper, we present two innovative spintronic computing primitives, i.e. spintronic approximate logic and spintronic stochastic neural network, which both leverage the intrinsic spintronic device physics to achieve much more compact and efficient designs than CMOS counterparts. In spintronic approximate logic, we employ the intrinsic current-mode thresholding operation to implement an accuracy-configurable adder and further demonstrate its application in approximate DSP applications. In spintronic stochastic neural networks, we leverage the stochastic properties of domain wall devices and magnetic tunnel junction to implement a low-power and robust artificial neural network design.