Additive manufacturing (AM) techniques have gained interest in the tissue engineering field, thanks to their versatility and unique possibilities of producing constructs with complex macroscopic geometries and defined patterns. Recently, composite materials-namely, heterogeneous biomaterials identified as continuous phase (matrix) and reinforcement (filler)-have been proposed as inks that can be processed by AM to obtain scaffolds with improved biomimetic and bioactive properties. Significant efforts have been dedicated to hydroxyapatite (HA)-reinforced composites, especially targeting bone tissue engineering, thanks to the chemical similarities of HA with respect to mineral components of native mineralized tissues. Herein, applications of AM techniques to process HA-reinforced composites and biocomposites for the production of scaffolds with biological matrices, including cellular tissues, are reviewed. The primary outcomes of recent investigations in terms of morphological, structural, and in vitro and in vivo biological properties of the materials are discussed. The approaches based on the nature of the matrices employed to embed the HA reinforcements and produce the tissue substitutes are classified, and a critical discussion is provided on the presented state of the art as well as the future perspectives, to offer a comprehensive picture of the strategies investigated as well as challenges in this emerging field of materiomics.