Hyperspectral and multispectral information processing systems and technologies have demonstrated its usefulness for the improvement of agricultural productivity and practices by providing useful information to farmers and crop managers on the factors affecting crop status and growth. These technologies are widely used in a range of agriculture applications such as crop management, crop yield forecasting, crop disease detection, and the monitoring of agriculture land usage, water, and soil conditions. Hyperspectral information sensing can acquire several hundred spectral bands that cover the electromagnetic spectrum of an observational scene in a single acquisition. The resulting hyperspectral data cube contains a large volume of spatial and spectral information. The hyperspectral sequence of images or video further increases the data generation velocity and volume which lead to the Big data challenges particularly in agricultural remote sensing applications. This paper is structured to first give a comprehensive review of representative studies to provide insights into significant research efforts in agriculture using Big data, machine learning and deep learning with the focus on frameworks or architectures, information processing and analytics with hyperspectral and multispectral data. The potential for utilizing Big data, machine learning and deep learning for hyperspectral and multispectral data in agriculture is very promising. The paper then further explores the potential of using ensemble machine learning and scalable parallel discriminant analysis which takes into consideration the spatial and spectral components for Big data in agriculture. To the best of our knowledge, no similar review study on agriculture with Big data, machine learning and deep learning for hyperspectral and multispectral information processing has been reported. Furthermore, the potential of ensemble machine learning and scalable parallel discriminant analysis has not been explored in agriculture information processing. Experiments and data analytics have been performed on hyperspectral data from agriculture for validation. The results have shown the good performance of our approach.