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We review the recent developments in obtaining accelerating cosmologiesand/or inflation from higher-dimensional gravitational theories, in particularsuperstring theories in ten dimensions and M-theory in eleven dimensions. Wefirst discuss why it is difficult to obtain inflationary behavior in theeffective low-energy theories of superstring/M-theory, i. e. supergravitytheories. We then summarize interesting solutions including S-branes that giverise to accelerating cosmologies and inflationary solutions in M-theory withhigher order corrections. Other approaches to inflation in the string contextare also briefly discussed.Comment: 38 pages, Invited review to be published in IJMPA, v2: slightly  expanded and refs. added, v3, v4: typos corrected, published versio

ACCELERATING COSMOLOGIES AND INFLATION FROM M/SUPERSTRING THEORIES