This paper focuses on one of the most commonly encountered materials in our society, namely paper. Paper is an inherently complex material, yet its use provides for chemical analysis approaches that are elegant in their simplicity of execution. In the first half of the previous century, paper in scientific research was used mainly for filtration and chromatographic separation. While its use decreased with the rise of modern elution chromatography, paper remains a versatile substrate for low-cost analytical tests. Recently, we have seen renewed interest to work with paper in (bio)analytical science, a result of the growing demand for inexpensive, portable analysis. Dried blood spotting, paper microfluidics, and paper spray ionization are areas in which paper is (re)establishing itself as an important material. These research areas all exploit several properties of paper, including stable sample storage, passive fluid movement and manipulation, chromatographic separation/extraction, modifiable surface and/or volume, easily altered shape, easy transport, and low cost. We propose that the real, and to date underexploited, potential of paper lies in utilizing its combined characteristics to add new dimensions to paper-based (bio)chemical analysis, expanding its applicability. This article provides the reader with a short historical perspective on the scientific use of paper and the developments that led to the establishment of the aforementioned research areas. We review important characteristics of paper and place them in a scientific context in this descriptive, yet critical, assessment of the achieved and the achievable in paper-based analysis. The ultimate goal is the exploration of integrative approaches at the interface between the different fields in which paper is or can be used.