The new approach of the global bifurcation analysis of strongly nonlinear dynamic problems based on the ideas of the so-called method of complete bifurcation groups is discussed. This approach allows for nonlinear models with a finite number of degrees of freedom to find, when system parameters are changing, new previously unknown stable regimes, in addition to the well-known, in particular, rare regular and chaotic attractors. In this paper, the main ideas of the method of complete bifurcation groups are discussed and the concept of complete and incomplete bifurcation diagrams is illustrated. Author considers a new point of view to the role of unstable solutions (regimes) for the problems of local and global analysis of strongly nonlinear dynamical systems. Simple examples of typical problems of nonlinear oscillations and nonlinear dynamics, illustrating the basic ideas and possibilities of the method of complete bifurcation groups, are given.