A systematic and efficient multimodal transfer-matrix approach is proposed for the comprehensive Bloch analysis of general 1-D/2-D/3-D periodic structures. We provide a linearization procedure for transforming the original nonlinear eigenvalue problem associated with 2-D/3-D structures to a standard one that can easily be solved without the need of a zero-searching algorithm in the complex plane. The proposed approach has been validated with bounded/open structures with complex geometries and/or inhomogeneous lossless/lossy materials. It demonstrates a significantly reduced computational time and leverages the strengths of full-wave simulators to deal with general problems and ad hoc quasi-analytical methods to give a fundamental understanding of the behavior of the structure. Also, it allows for an accurate evaluation of the imaginary part of the wavenumber, which offers information of material dissipation, stopband rejection, leakage, and complex modes.