We study correlation functions of a conserved spin-1 current J µ in three dimensional Conformal Field Theories (CFTs). We investigate the constraints imposed by permutation symmetry and current conservation on the form of three point functions J µ J ν O ∆, and the four point function J µ J ν J ρ J σ and identify the minimal set of independent crossing symmetry conditions. We obtain a recurrence relation for conformal blocks for generic spin-1 operators in three dimensions. In the process, we improve several technical points, facilitating the use of recurrence relations. By applying the machinery of the numerical conformal bootstrap we obtain universal bounds on the dimensions of certain light operators as well as the central charge. Highlights of our results include numerical evidence for the conformal collider bound and new constraints on the parameters of the critical O(2) model. The results obtained in this work apply to any unitary, parity-preserving three dimensional CFT. arXiv:1705.04278v1 [hep-th] 11 May 2017 J J p O q J J , (1.2) where λ (p) JJO are the coefficients of the operator O in the OPE of two currents. The index p, q run over a finite range, which depends on the spin and parity of the operator O. The symbolstands for the conformal blocks that are labeled by p, q and the quantum numbers ∆, and parity of O. This is described in detail in section 2. Following the usual bootstrap strategy, we then impose crossing symmetry of this four-point function. However, due to current conservation, not all crossing equations are linearly independent. In section 2, we explain how to select a minimal set of independent crossing equations to be imposed 7 See for instance (2.54) in the next section. 8 In fact, we used this to cross check the computation of the conformal blocks. 9 In fact, this is true for a generic choice of time coordinate around the point u = v = 1/4. The exception being the coordinate y. In this special case, the rank of [K y ] is 10.where the operators J i have spin 1 and dimension ∆ i and O ± are operators with spin dimension ∆ and parity ±.