This paper generalizes the concepts of fuzzy metric spaces, introduced by Kramosil and Michalek, and by George and Veeramani, to the quasi-metric setting. It shows that every quasi-metric induces a fuzzy quasi-metric and, conversely, every fuzzy quasi-metric space generates a quasi-metrizable topology. The paper discusses basic properties of fuzzy quasi-metric spaces, including their relationship with quasi-uniformities and quasi-metric spaces. It defines KM-fuzzy quasi-pseudo-metric and GV-fuzzy quasi-pseudo-metric spaces, and explores their properties. The paper also introduces the concept of bicompleteness in fuzzy quasi-metric spaces and discusses the problem of completing fuzzy metric spaces. It shows that every quasi-metrizable topological space admits a compatible GV-fuzzy quasi-metric, and that the topology generated by a KM-fuzzy quasi-metric space is quasi-metrizable. The paper also presents results on the bicompletion of fuzzy quasi-metric spaces and the existence of isometries between them.This paper generalizes the concepts of fuzzy metric spaces, introduced by Kramosil and Michalek, and by George and Veeramani, to the quasi-metric setting. It shows that every quasi-metric induces a fuzzy quasi-metric and, conversely, every fuzzy quasi-metric space generates a quasi-metrizable topology. The paper discusses basic properties of fuzzy quasi-metric spaces, including their relationship with quasi-uniformities and quasi-metric spaces. It defines KM-fuzzy quasi-pseudo-metric and GV-fuzzy quasi-pseudo-metric spaces, and explores their properties. The paper also introduces the concept of bicompleteness in fuzzy quasi-metric spaces and discusses the problem of completing fuzzy metric spaces. It shows that every quasi-metrizable topological space admits a compatible GV-fuzzy quasi-metric, and that the topology generated by a KM-fuzzy quasi-metric space is quasi-metrizable. The paper also presents results on the bicompletion of fuzzy quasi-metric spaces and the existence of isometries between them.