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Gravitational waves emitted from the coalescence of neutron star binariesopen a new window to probe matter and fundamental physics in unexplored,extreme regimes. To extract information about the supranuclear matter insideneutron stars and the properties of the compact binary systems, robusttheoretical prescriptions are required. We give an overview about generalfeatures of the dynamics and the gravitational wave signal during the binaryneutron star coalescence. We briefly describe existing analytical and numericalapproaches to investigate the highly dynamical, strong-field region during themerger. We review existing waveform approximants and discuss properties andpossible advantages and shortcomings of individual waveform models, and theirapplication for real gravitational-wave data analysis.

Interpreting Binary Neutron Star Mergers: Describing the Binary Neutron Star Dynamics, Modelling Gravitational Waveforms, and Analyzing Detections