In machine vision, the tasks of both the crowd counting and the crowd density estimation attracted a number of researchers from different research institutes throughout the world. These tasks are of significance importance while analyzing the surveillance videos and images both at the real and offline modes. A number of different conventional and modern algorithms are being applied to estimate the accurate amount of people from the crowd from the target image or video file but failed to provide the required results due to heterogeneity of the data instances. To resolve the issue, machine learning models like deep networks like Convolution Neural Network (CNN) and its variants were introduced. In this paper, a detailed and comprehensive review of the work related to both of the crowd counting and density estimation using deep network is provided in quite a very unique way to make it useful for the researchers working in the field of computer vision. Following are the salient features of our review that play key role in making our contribution worthwhile and unique among the surveys and reviews of similar kind: (i) our survey intends to classify the noteworthy literature with respect to the application and the tasks related to crowd counting and density estimation, (ii) the survey also tried to cover in-depth contributions in crowd counting existing works at different level like images or videos (iii) this state-of-the-art review covers each article in the following dimensions: the designated task performed, source level, results obtained, features used, and (iv) lastly it concludes the summary of the related articles according to the publishing years, related tasks (or subtasks), and types of classifiers used. In the end, major challenges and tasks related to crowd counting and density estimation in computer vision are also discussed.