Over the years, advances in sensor technologies have enhanced spatial, temporal, spectral, and radiometric resolutions, thus significantly improving the size, resolution, and quality of imagery. These vast developments have inspired improvement in various hyperspectral images (HSI) classification applications such as land cover mapping, vegetation classification, urban monitoring, and understanding which are essential for better utilization of Earth’s resources. HSI classification requires superior algorithms with greater accuracy, less computational complexity, and robustness to extract rich, spectral-spatial information. Deep convolution neural networks (DCCNs) have revolutionized image classification experience, with robust architectures being proposed from time to time. However, insufficient training samples have been earmarked as a significant bottleneck for supervised HSI classification and have not been fully explored in literature. To stimulate further research, this paper reviews current methods that handle labeled data insufficiency and the current feature learning methods for HSI classification using DCNNs. It also presents various methods’ results on the three most popular public HSI datasets, together with intuitive observations motivating future research by the hyperspectral community.