Additively manufactured (AM, =3D printed) porous metallic biomaterials with topologically ordered unit cells have created a lot of excitement and are currently receiving a lot of attention given their great potential for improving bone tissue regeneration and preventing implant-associated infections. This paper presents an overview of the various aspects of design, manufacturing, and bio-functionalization of these materials from a "designer material" viewpoint and discusses how rational design principles could be used to topologically design the underlying lattice structures in such a way that the desired properties including mechanical properties, fatigue behavior, mass transport properties (e.g., permeability, diffusivity), surface area, and geometrical features affecting the rate of tissue regeneration (e.g., surface curvature) are simultaneously optimized. We discuss the different types of topological design including those based on beam-based unit cells, sheet-based unit cells (e.g., triply periodic minimal surfaces), and functional gradients. We also highlight the use of topology optimization algorithms for the rational design of AM porous biomaterials. The topology-property relationships for all of the above-mentioned types of properties are presented as well followed by a discussion of the applicable AM techniques and the pros and cons of different types of base materials (i.e., bioinert and biodegradable metals). Finally, we discuss how the huge (internal) surfaces of AM porous biomaterials and their pore space could be used respectively for surface bio-functionalization and accommodation of drug delivery vehicles so as to enhance their bone tissue regeneration performance and minimize the risk of implant-associated infections. We conclude with a general discussion and by suggesting some possible areas for future research.