Spintronic nanodevices have ultrafast nonlinear dynamic and recurrence behaviors on a nanosecond scale that promises to enable spintronic reservoir computing (RC) system. Here two physical RC systems based on a single magnetic skyrmion memristor (MSM) and 24 spin-torque nano-oscillators (STNOs) were proposed and modeled to process image classification task and nonlinear dynamic system prediction, respectively. Based on our micromagnetic simulation results on the nonlinear responses of MSM and STNO with current pulses stimulation, the handwritten digits recognition task domesticates that an RC system using one single MSM has the outstanding performance on image classification. In addition, the complex unknown nonlinear dynamic problems can also be well solved by a physical RC system consisted of 24 STNOs confirmed in a second-order nonlinear dynamic system and NARMA10 tasks. The capability of both high accuracy and fast information processing promises to enable one type of brain-like chip based on spintronics for various artificial intelligence tasks.