The findings of ferromagnetic superconductor have attracted much attention not only for fundamental research to investigate how the antagonistic properties of ferromagnetism and superconductivity coexist peacefully but also for potential technological applications. Firstly, in order to help for understanding the ferromagnetic superconductor, I have explained the orbital and paramagnetic pair-breaking effects of magnetic field, which breaks the superconducting Cooper pairs. In addition to such effects of magnetic field, the singlet Cooper pairs become unstable upon going through the ferromagnetic materials by the proximity effect. The proximity effect occurs at the interface of thin films composing of superconductor and ferromagnet and leads to have very short penetration depth of Cooper pairs. However, a type of odd-frequency triplet in comparison with the singlet could be very stable and has a longer effective depth. It needs to be explored for the innovative spintronic devices. Finally, various ferromagnetic superconductors coexist and the lower-dimensional materials under the Quantum confinement effect have been introduced.