Research on big data analytics is entering in the new phase called fast data where multiple gigabytes of data arrive in the big data systems every second. Modern big data systems collect inherently complex data streams due to the volume, velocity, value, variety, variability, and veracity in the acquired data and consequently give rise to the 6Vs of big data. The reduced and relevant data streams are perceived to be more useful than collecting raw, redundant, inconsistent, and noisy data. Another perspective for big data reduction is that the million variables big datasets cause the curse of dimensionality which requires unbounded computational resources to uncover actionable knowledge patterns. This article presents a review of methods that are used for big data reduction. It also presents a detailed taxonomic discussion of big data reduction methods including the network theory, big data compression, dimension reduction, redundancy elimination, data mining, and machine learning methods. In addition, the open research issues pertinent to the big data reduction are also highlighted.