Video description is the automatic generation of natural language sentences that describe the contents of a given video. It has applications in human-robot interaction, helping the visually impaired and video subtitling. The past few years have seen a surge of research in this area due to the unprecedented success of deep learning in computer vision and natural language processing. Numerous methods, datasets, and evaluation metrics have been proposed in the literature, calling the need for a comprehensive survey to focus research efforts in this flourishing new direction. This article fills the gap by surveying the state-of-the-art approaches with a focus on deep learning models; comparing benchmark datasets in terms of their domains, number of classes, and repository size; and identifying the pros and cons of various evaluation metrics, such as SPICE, CIDEr, ROUGE, BLEU, METEOR, and WMD. Classical video description approaches combined subject, object, and verb detection with template-based language models to generate sentences. However, the release of large datasets revealed that these methods cannot cope with the diversity in unconstrained open domain videos. Classical approaches were followed by a very short era of statistical methods that were soon replaced with deep learning, the current state-of-the-art in video description. Our survey shows that despite the fast-paced developments, video description research is still in its infancy due to the following reasons: Analysis of video description models is challenging, because it is difficult to ascertain the contributions towards accuracy or errors of the visual features and the adopted language model in the final description. Existing datasets neither contain adequate visual diversity nor complexity of linguistic structures. Finally, current evaluation metrics fall short of measuring the agreement between machine-generated descriptions with that of humans. We conclude our survey by listing promising future research directions.