The majority of stars born in dense stellar clusters are part of binary star systems. Circumbinary discs of gas and dust commonly surround binary star systems and are responsible for accreting material onto the binary. The gas flow dynamics from the circumbinary disc onto the binary components have significant implications for planet formation scenarios in binary systems. Misalignments between the circumbinary disc and the binary orbital plane are commonly observed. A misaligned circumbinary disc undergoes nodal precession. For a low initial inclination, the precession is around the binary angular momentum vector, while for a sufficiently high initial inclination, the precession is around the eccentricity vector. Dissipation causes the disc to evolve to align coplanar to the binary orbital plane or perpendicular (i.e., polar) to the binary orbital plane. I present 3-dimensional hydrodynamical simulations and linear theory on the evolution of highly misaligned circumbinary discs. I show that polar-aligned circumbinary discs are favorable environments for forming polar circumbinary (P-type) planets. Moreover, misaligned and polar circumbinary material flows around each binary component, forming misaligned and polar circumstellar discs. These circumstellar discs undergo long-lived Kozai-Lidov oscillations that may prompt the formation of giant circumstellar (S-type) planets in binary star systems. The evolution of protoplanetary discs in and around binary star systems bears important implications for planet formation.