After a brief review of post-Newtonian theory, I will present the result for the 4.5PN flux and will focus more particularly on the computation of a particular hereditary effect in the multipolar post-Minkowskian iteration, the "tails of memory". I will show how the techniques developed for this can be applied to the computation of the "cubic memory", which could potentially give rise to a "memory distortion" effect, similar to the one recently discovered in the self-force context. In the second part of my talk, I will review the PN computations of the fluxes for eccentric orbits, as well as its gauge-invariant formulation. For that, I will present the computation of 4PN periastron advance for eccentric orbits. Finally, I will discuss how these results enter hybrid models, and the current challenges we are encountering.