A critical constraint in the design of appropriate medical devices for the lowest-resource settings is the lack of access to maintenance or repair on instrumentation. There are numerous point-of-care applications for which quantitative readout would have clinical utility. Thus, a challenge to the device developer is to enable quantitative device readout in an equipment-free model that is appropriate for use in even the lowest-resource settings. Paper microfluidics has great potential for enabling equipment-free devices that are low-cost, operable by minimally-trained users, and provide quantitative readout. The focus of this critical review is to describe the work, starting several decades ago and continuing to the present, to enable assays with quantitative readout in a fully-disposable device.