<p style='text-indent:20px;'>In this paper, we study the existence of radial and nonradial solutions to the scalar field equations with fractional operators. For radial solutions, we prove the existence of infinitely many solutions under <inline-formula><tex-math id="M1">\begin{document}$ N \geq 2 $\end{document}</tex-math></inline-formula>. We also show the existence of least energy solution (with the Pohozaev identity) and its mountain pass characterization. For nonradial solutions, we prove the existence of at least one nonradial solution under <inline-formula><tex-math id="M2">\begin{document}$ N \geq 4 $\end{document}</tex-math></inline-formula> and infinitely many nonradial solutions under either <inline-formula><tex-math id="M3">\begin{document}$ N = 4 $\end{document}</tex-math></inline-formula> or <inline-formula><tex-math id="M4">\begin{document}$ N \geq 6 $\end{document}</tex-math></inline-formula>. We treat both of the zero mass and the positive mass cases.