Cluster structures can be stable in the interior of atomic nuclei. The study of α-cluster structure of atomic nuclei and its effects are important topics in nuclear physics as well as astrophysics. In the past few decades, cluster structure effects in atomic nuclei have been much studied for heavy-ion nuclear reactions. This paper summarizes the authors' studies on the α-cluster structure effects on nuclei in nuclear reactions and relativistic heavy-ion collisions. For example, the cluster structure of atomic nuclei has been studied through giant resonances of atomic nuclei. The cluster structure of the nucleus is studied through the emission and correlation of particles (including neutrons, protons, and photons) in nuclear reactions and through collective flows. We extend the cluster effect of atomic nuclei to relativistic heavy-ion collisions, e.g., to the study of collective flows and their rise and fall, the HBT (Hanbury Brown and Twiss) correlation, multiplicity correlations, the dihadron azimuthal correlation, and electromagnetic fields.