This second special issue of Pure and Applied Geophysics in honor of Keiiti Aki focuses on recent advances in quantifying and interpreting heterogeneities in lithosperic structures and earthquake behavior. The volume provides a combination of reviews, methodological studies and applications on topics related to Aki's pioneering contributions. It also includes material on Keiiti Aki and a list of his publications. The discussed subjects include research associated with dynamic earthquake rupture, studies on imaging earthquake locations and structures using P and S seismic phases, and studies associated with imaging source and structure properties using scattered coda waves. The volume will be useful to students and researchers alike, who are interested in the nature of large- and small-scale heterogeneities in the earth's lithosphere and earthquake properties.Ben-Zion, Yehuda is the author of 'Advances in Studies of Heterogeneities in the Earth's Lithosphere The Keiiti Aki', published 2006 under ISBN 9783764375799 and ISBN 3764375795.