The Story Of Design, by Charlotte and Peter Fiell, is billed as "the first ever comprehensive account of the fascinating, multi-stranded story of design, from its earliest beginnings right up to the present day." It does indeed provide an overview of the entire history of design, from Paleolithic tools to the iPhone.
The Story Of Design's approach is similar to that of David Raizman's History Of Modern Design, though the Fiells' book is especially significant as its scope also extends to pre-industrial design. Like Raizman, the Fiells focus largely on American, European, and Japanese design, whereas the recent History Of Design (which begins in 1400) is more global in its coverage.
The Fiells previously co-wrote two A-Z design books for Taschen: Design Of The 20th Century and Industrial Design A-Z. The Story Of Design, with 500 pages and hundreds of large illustrations, is an excellent general introduction to design history. It has footnotes, though there's no bibliography.