I will present a new approach to the construction of Baxter Q-operators based on their intimate relation with the theory of Yangians. New solutions of the Yang-Baxter equation connected with harmonic oscillator algebra serve as building blocks for other solutions via the standard fusion procedure. This mechanism allows to derive the full hierarchy of operatorial functional equations for all commuting transfer matrices and Q-operators. The method is first applied to sl(n $\vert$ m) symmetric spin chains with fundamental representation in quantum space but can be generalized to any representation (including non-compact) in quantum space. The present study is motivated by the need of a better understanding of AdS/CFT integrability.