Magnetic quantum critical point (QCP) arises when a long-range magnetic order occurring at finite temperature can be suppressed to absolute zero temperature by using chemical substitutions or exerting high pressure. Exotic phenomena such as the non-Fermi-liquid behaviors or the unconventional superconductivity are frequently observed near the magnetic QCP. In comparison with chemical substitutions, the application of high pressure has some advantages in the sense that it introduces no chemical disorder and can approach the QCP in a very precise manner. In this article, our recent progress in exploring the unconventional superconductors in the vicinity of pressure-induced magnetic QCP is reviewed. By utilizing the piston-cylinder and cubic-anvil-cell apparatus that can maintain a relatively good hydrostatic pressure condition, we first investigated systematically the effect of pressure on the electrical transport properties of the helimagnetic CrAs and MnP. We discovered for the first time the emergence of superconductivity below Tc=2 K and 1 K near their pressure-induced magnetic QCPs at Pc0.8 GPa and 8 GPa for CrAs and MnP, respectively. They represent the first superconductor among the Cr- and Mn-based compounds, and thus open a new avenue to searching novel superconductors in the Cr- and Mn-based systems. Then, we constructed the most comprehensive temperature-pressure phase diagram of FeSe single crystal based on detailed measurements of high-pressure resistivity and alternating current magnetic susceptibility. We uncovered a dome-shaped magnetic phase superseding the nematic order, and observed the sudden enhancement of superconductivity with Tcmax=38.5 K accompanied with the suppression of magnetic order. Our results revealed explicitly the competing nature of nematic order, antiferromagnetic order, and superconductivity, and how the high-Tc superconductivity is achieved by suppressing the long-range antiferromagnetic order, suggesting the important role of antiferromagnetic spin fluctuations for the Cooper paring. These aforementioned results demonstrated that high pressure is an effective approach to exploring or investigating the anomalous phenomena of strongly correlated electronic systems by finely tuning the competing electronic orders.