We will discuss a remarkable family of holomorphic Poisson structures on projective spaces, discovered by Feigin and Odesskii. These are given by a normal elliptic curve E inside CP^n and a vector field on E. First, I will introduce them, describe where the Poisson structure drops its rank, and other relevant properties. Then I will proceed to an alternative way of defining/describing the structure, by resolving the secant variety of E, constructing a natural co-Higgs bundle there, and producing a Poisson structure out of the co-Higgs bundle. This is meant to be a widely accessible talk, I will try to give all the relevant definitions/facts.