Seated recently in the special collections room at the Massachusetts Institute of Technology library, Anders Fernstedt raced through an imposing set of yellowing articles and correspondence.

Several years ago Mr. Fernstedt, an independent Swedish scholar who is studying the work of the 20th-century philosopher Karl Popper and several of his colleagues, would have scratched out notes and set aside documents for photocopying.

Now, however, his tool of choice is the high-resolution camera on his iPhone. When he found a document of interest, he quickly snapped a photo and instantly shared his discovery with a colleague working hundreds of miles away. Indeed, Mr. Fernstedt, who conducts his research on several continents, now packs his own substantial digital Popper library on the disk of his MacBook Air laptop computer — more than 50,000 PDF files that he can browse through in a flash.

In just a few years, advances in technology have transformed the methods of historians and other archival researchers. Productivity has improved dramatically, costs have dropped and a world distinguished by solo practitioners has become collaborative. In response, developers are producing an array of computerized methods of analysis, creating a new quantitative science....