With contributions from top geographers, this Companion frames sustainability as exemplar of transdisciplinary science (critical geography) while improving future scenarios, debating perspectives between rich North/poor South, modern urban/backwards rural, and everything in between. The Companion has five sections that carry the reader from foundational considerations to integrative trends, to resources use and accommodation, to examples highlighting non-traditional pathways, to a postscript about cooperation of the industrialized Earth and a prognosis of the road ahead for the new geographies of sustainability.