One of the most critical challenges for today's and future data-intensive and big-data problems is data storage and analysis. This paper first highlights some challenges of the new born Big Data paradigm and shows that the increase of the data size has already surpassed the capabilities of today's computation architectures suffering from the limited bandwidth, programmability overhead, energy inefficiency, and limited scalability. Thereafter, the paper introduces a new memristor-based architecture for data-intensive applications. The potential of such an architecture in solving data-intensive problems is illustrated by showing its capability to increase the computation efficiency, solving the communication bottleneck, reducing the leakage currents, etc. Finally, the paper discusses why memristor technology is very suitable for the realization of such an architecture; using memristors to implement dual functions (storage and logic) is illustrated.@en