This presentation focuses on the development of tailored reduced-order models (ROMs) designed for bifurcating nonlinear parametric partial differential equations (PDEs). In this framework, multiple solutions can emerge for a given physical and/or geometrical parametric instance. Traditional certified reduced basis techniques struggle to accurately represent bifurcating phenomena, as error estimations become unreliable when bifurcations occur. Consequently, ROMs for bifurcating nonlinear PDEs have primarily relied on data compression strategies, such as proper orthogonal decomposition. The primary objective of the talk is to propose an innovative tailored greedy algorithm for bifurcating nonlinear PDEs based on deflation-based strategies. These algorithms can (i) simultaneously certify multiple behaviors of the system through the deflated-greedy approach and (ii) identify the parameter responsible for the non-uniqueness of the solution through an adaptive greedy approach, even when provided with limited information about the parametric space. The deflated-greedy method leverages various techniques, including deflation and continuation, to enrich the reduced space with bifurcating solutions. On the other hand, the adaptive-greedy approach exploits the non-differentiability of the solution with respect to the bifurcating parameter. The effectiveness of these strategies is tested on the Navier-Stokes equations in a sudden expansion channel, featuring three coexisting solutions for a single parameter. The results are compared in terms of accuracy and error certification against the high-fidelity solution, contrasting with standard greedy and proper orthogonal decomposition methods. This talk show results from works with several collaborators: F. Ballarin, C. Canuto, T. Chacòn Rebollo, M. Girfoglio, A. Ivagnes, T. Iliescu, G. Rozza.