Research regarding topological Dirac and Weyl semimetals contributes to our understanding not only of the field of solid-state physics, but also the field of high-energy physics as the physics of Dirac and Weyl semimetals resembles the physics of Dirac and Weyl massless fermions. In condensed matter physics, the Weyl nodes are detached in momentum space and may be realized as emergent quasiparticles with a distinct chirality, left-handed or right-handed. These states lead to phenomena like the chiral anomaly and the anomalous Hall effect (AHE). Furthermore, the combination of quantum effects and magnetic effects in magnetic Weyl semimetals is very intriguing. Magneto-optical tools, which are usually used to study magnetic phenomena, also contribute to magnetic Weyl semimetals. Moreover, with the magneto-optical technique, it is possible to follow the dynamics of the processes and to study the lifetime of the Weyl states. In this work, we review and discuss the effects of using magneto-optical tools for studying quantum effects like the chiral anomaly or magnetic effects in magnetic Weyl and Dirac systems using the magneto-optical Kerr effect (MOKE) or Faraday systems including a single detection and imaging. Examples of using magneto-optical systems in the research of ultrafast magnetic dynamics of thin polycrystalline nickel and permaloy are reviewed as are the magnetic spatial dynamics by employing magneto-optical Kerr or Faraday microscopy tools with ferromagnetic thin films. Interestingly, the excitation of a circularly polarized femtosecond laser pulse could lead to the breakage of time-reversal symmetry and to the transformation of the Dirac state to the Floquet–Weyl semimetal state. The development of a suitable ultrafast magneto-optical system for Weyl systems is discussed, and the practical difficulties for the realization of such a system are considered.