We present a highly general interior point method for non-symmetric conic optimization and its Matlab implementation. The algorithm can solve optimization problems over a cone as long as the user can supply the gradient and Hessian of a logarithmically homogeneous self-concordant barrier for either the cone or its dual. We outline three applications: hyperbolic programming, sum-of-squares optimization without semidefinite programming, and bounding polynomials using nonnegative circuit polynomials.