A large variety of microorganisms produce molecules to communicate via complex signaling mechanisms such as quorum sensing and chemotaxis. The biological diversity is enormous, but synthetic inanimate colloidal microswimmers mimic microbiological communication (synthetic chemotaxis) and may be used to explore collective behaviour beyond the one-species limit in simpler setups. In this work we combine particle based and continuum simulations as well as linear stability analyses, and study a physical minimal model of two chemotactic species. We observed a rich phase diagram comprising a "hunting swarm phase", where both species self-segregate and form swarms, pursuing, or hunting each other, and a "core-shell-cluster phase", where one species forms a dense cluster, which is surrounded by a (fluctuating) corona of particles from the other species. Once formed, these clusters can dynamically turn inside out, representing a "species-reversal". These results exemplify a physical route to collective behaviours in microorganisms and active colloids, which are so-far known to occur only for comparatively large and complex animals like insects or crustaceans.Chemotaxis -the movement of organisms in response to a chemical stimulus -allows them to navigate in complex environments, find food and avoid repellants. It is involved in many biological processes where microorganisms (or cells) coordinate their motion; these include wound healing, fertilization, pathogenic invasion of a host, and bacterial colonization [1, 2]. In such cases, microorganisms are attracted (or repelled) by certain substances (chemoattractants/ chemorepellents), but they are also attracted to chemicals produced by other microorganisms (or cells), such as cAMP in the case of Dictyostelium cells [3] or autoinducers in signaling Escherichia coli [4], which leads to chemical interactions (communication) among the microorganisms.While many existing models studying microbiological chemotaxis (or chemical interactions) focus on a single species [5][6][7][8][9][10][11][12], the typical situation in the microbiological habitat is that various different species simultaneously produce certain chemicals to which others respond via chemotaxis or based on quorum sensing mechanisms. One simple example involving chemical signaling across species is provided by macrophage-facilitated breast cancer cell invasion which has recently been modeled [13]. There, tumor cells attract macrophages, which are certain white blood cells normally playing a key role in the human immune system. They then control the physiological function of the macrophages and exploit their abilities. More specifically, the tumor cells produce the colony-stimulating factor (CSF-1) leading to the attraction and growth of macrophages which in turn release epidermal growth factors (EGF) resulting in the growth and mobility increase of the tumor cells (see Fig. 1).Similarly to microorganisms, synthetic inanimate colloids, coated with a material which catalyzes a certain reaction on (a part of) their surfa...