Video classification task has gained a significant success in the recent years. Specifically, the topic has gained more attention after the emergence of deep learning models as a successful tool for automatically classifying videos. In recognition to the importance of video classification task and to summarize the success of deep learning models for this task, this paper presents a very comprehensive and concise review on the topic. There are a number of existing reviews and survey papers related to video classification in the scientific literature. However, the existing review papers are either outdated, and therefore, do not include the recent state-of-art works or they have some limitations. In order to provide an updated and concise review, this paper highlights the key findings based on the existing deep learning models. The key findings are also discussed in a way to provide future research directions. This review mainly focuses on the type of network architecture used, the evaluation criteria to measure the success, and the data sets used. To make the review self- contained, the emergence of deep learning methods towards automatic video classification and the state-of-art deep learning methods are well explained and summarized. Moreover, a clear insight of the newly developed deep learning architectures and the traditional approaches is provided, and the critical challenges based on the benchmarks are highlighted for evaluating the technical progress of these methods. The paper also summarizes the benchmark datasets and the performance evaluation matrices for video classification. Based on the compact, complete, and concise review, the paper proposes new research directions to solve the challenging video classification problem.