In this chapter, parabola-saddles, third-order centers and saddles, and hyperbolic singular flows in the crossing and product cubic systems are presented, and the corresponding switching dynamics are discussed through infinite equilibriums in such cubic systems. The parabola-saddles are the appearing and switching bifurcations of the saddle and center. The third-order centers are the appearing bifurcations of the center, saddle, and center. The third-order saddles are the appearing bifurcations of the saddle, center, and saddle. The hyperbolic singular flows are the appearing bifurcations of hyperbolic and hyperbolic-secant flows. The infinite equilibriums in such a cubic system include up-down-hyperbolic upper-to-lower saddles, parabola-saddles, parabola-hyperbolic, and circular upper-to-lower saddles. The up-down hyperbolic upper-to-lower saddles are the switching bifurcations of hyperbolic singular flows with a saddle and center. The parabola-saddles are the switching bifurcations of parabola-saddles with hyperbolic-to-hyperbolic-secant flows. The parabola-hyperbolic and circular upper-to-lower saddles are the switching bifurcations of a third-order saddle with a hyperbolic-to-hyperbolic-secant flow and a third-order center with a hyperbolic-secant-to hyperbolic flow.