In this review, we provide a comprehensive overview of additive manufacturing (AM) technologies and materials as well as design possibilities to manufacture metamaterials for a variety of biomedical applications, of which many are inspired by nature itself. It is described that how new AM technologies (such as continuous liquid interface production and multiphoton polymerization) and new developments in more mature AM technologies (such as powder bed fusion, stereolithography and extrusion-based bioprinting) have led to more precise, efficient, and personalized biomedical components. Extrusion-based bioprinting, specifically, is a revolutionary topic creating intricate models with remarkable mechanical compatibility of metamaterials, such as negative/zero Poisson's ratio and stress elimination for tissue engineering and regenerative medicine. By exploiting a variety of designs for porous structures (such as truss, triply periodic minimal surface, and plant/animal-inspired and functionally graded lattices), AM made bioactive bone implants, artificial tissues and organs are made for tissue replacement purposes. The material palette of the AM metamaterials has also become very diverse nowadays ranging from metals and alloys (such as titanium and cobalt-chromium alloys) to polymers (like biodegradable polycaprolactone (PCL) and polymethyl methacrylate (PMMA)) which could be even integrated within bioactive bioceramics. These advancements are driving the progress of biomedical technology, improving human health and quality of life for future generations.