Since Andreas Manz first introduced the microchip technology for chemical applications back in the 1990s, the field of ‘microfluidics’ has expanded widely and microfluidic tools have become ubiquitous in life sciences research. However, pumps and controllers associated with most current microfluidic chips continue to be bulky and costly. A new class of microfluidic devices in which flow channels are composed of multidimensional (2D or 3D) shapes of porous materials is becoming increasingly popular. The ability of porous materials to wick fluids obviates the need for pumps, making such devices portable, low-cost, and ideal for use in low-resource settings. Such devices are broadly referred to as “paper microfluidic devices”. The ability to manipulate fluids in paper microfluidics has progressively increased over the past decade and such devices are currently being used to develop highly sensitive and multiplexed low-cost diagnostic/sensing devices. In this article, we review the area of paper microfluidics covering the basic fluid physics, methods of fabrication, flow control tools, applications in diagnostics/sensing, and applications in other emerging areas like tissue engineering and power storage. This review is targeted to a broad audience that does not have prior exposure to the field of paper-based microfluidics. Through this article, we wish to invite researchers from multiple backgrounds to contribute to further development in this new and exciting area of research.