We, for the first time, discuss the consequences of the critical end point (CEP) in relativistic nuclear collisions on the basis of the general theory of critical phenomena and discuss its traces in real experimental data at SPS and RHIC. Theoretically, a lot of evidence that there exists a CEP in the QCD phase diagram has been accumulating. Nevertheless, so far, no equation of state with the CEP has been explored in phenomenological analyses. We construct the equation of state with the CEP on the basis of the universality hypothesis and show that the CEP acts as an attractor of isentropic trajectories. We also consider the time evolution with the CEP on the basis of the theory of dynamical critical phenomena, and discuss how the CEP affects the final state observables (correlation length, fluctuation, chemical freezeout, kinetic freezeout). Finally, we argue that the anomalously low kinetic freezeout temperature at RHIC suggests the possibility of the existence of the CEP.