Counterflow flames provide an ideal platform for understanding the flame structure and as a model to study the effect of physical and chemical perturbations on the flame structure. This article reviews the advances made in the understanding of combustion dynamics and chemistry through experimental and numerical studies in counterflow non-premixed and partially premixed flames. Key contributions on fundamental aspects such as extinction, ignition and effect of perturbations on the stability of diffusion flames are first summarized and analysed. The review then focuses on the progress made in the understanding of the effect of inert particles and flame suppressants on the flame characteristics. A review of detailed studies on edge flames facilitates further understanding of local quenching and re-ignition phenomena in highly turbulent flames. The influence of radiation model and unsteady flow-conditions on the flame kinetics and dynamics along with work on NO x kinetics has been discussed. The review also outlines that specific experiments need to be carried out over a wide range of conditions for further understanding and validation of numerical models.