Motion estimation (ME) being a fundamental process of crowd behavior analysis experienced real challenges at high densities due to visual ambiguities and occlusion problems etc. Various surveys reported in the past years summarize conventional ME methods for crowd behaviors at low/medium densities. In this paper, we focus on state-of-the-art fluid dynamics (FD) ME methods developed over the last one and the half-decade for high-density crowd analysis. A detailed discussion is provided on the development of FD ME methods explaining the strengths and weaknesses and viability of FD ME methods for anomaly detection at high crowd densities. Comprehensive experiments are performed comparing the performance of conventional and FD ME at varying crowd densities. Experimentation results show that conventional ME methods fail at high-density crowd whereas FD ME methods could estimate motion only at the global level. Still, research is required to meet the challenges of local ME at high crowd densities. © 2020, © 2020 The Royal Photographic Society.