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Resonant inelastic x-ray scattering (RIXS) has been emerging as a promising probe to elucidate the excitation spectra of the electrons. In particular, we focus on the magnetic excitation of the system probed by RIXS. From a theoretical point of view, it is non-trivial to extract the magnetic excitation from the scattering process between the electrons and photons. For instance, different considerations are needed when we discuss the magnetic RIXS around the different absorption edges. We see that the treatment at the K-edge is straightforward, while that at the L edge needs an extra caution, which we overcome by introducing the projection method. In this talk, we briefly explain theoretical framework to investigate the magnetic RIXS spectra in transition-metal oxides at the K and L edges. It is applied to some cuprates and Sr₂IrO₄. We show that the calculated magnetic RIXS spectra capture the characteristic behaviors the experimental data exhibit. In addition, several predictions, such as the splitting of the excitation modes in Sr₂IrO₄ will be addressed.