The current paper is devoted to classification of powder-bed additive manufacturing (PB-AM) techniques and description of specific features, advantages and limitation of different PB-AM techniques in aerospace applications. The common principle of “powder-bed” means that the used feedstock material is a powder, which forms “bed-like” platform of homogeneous layer that is fused according to cross-section of the manufactured object. After that, a new powder layer is distributed with the same thickness and the “printing” process continues. This approach is used in selective laser sintering/melting process, electron beam melting, and binder jetting printing. Additionally, relevant issues related to powder raw materials (metals, ceramics, multi-material composites, etc.) and their impact on the properties of as-manufactured components are discussed. Special attention is paid to discussion on additive manufacturing (AM) of aerospace critical parts made of Titanium alloys, Nickel-based superalloys, metal matrix composites (MMCs), ceramic matrix composites (CMCs) and high entropy alloys. Additional discussion is related to the quality control of the PB-AM materials, and to the prospects of new approaches in material development for PB-AM aiming at aerospace applications.