Challenges in Gravitational-Wave Modelling of Compact Binary systems.

Compact binary systems are key sources of gravitational-waves (GWs), for both ground- and space-based  detectors. In order to detect GWs and extract their physical parameters, there is an ongoing scientific endeavour to model their strong relativistic motion in great detail. In addition, to analyse the forthcoming GW data, it will be essential to reduce the huge demand on computational resources needed to characterise observed GW sources by developing new techniques to analyse the data in a quick and efficient way.  In this talk I will revisit the current challenges in GW astronomy, and present recent works towards addressing these two pressing problems. In particular, I will focus on the computation of the gravitational self-force for waveform modelling, and the use of novel  techniques for enhancing and speeding-up parameter estimation analysis.