© 2015 IEEE. Finite-set statistics (FISST, a.k.a. random-set information fusion) was first systematically described in 2007 in the book Statistical Multisource-Multitarget Information Fusion. The purpose of this paper is to survey the most intriguing advnces in the field that have emerged in at least 19 nations since 2007, as reported in the 2014 sequel, Advances in Statistical Multisource-Multitarget Information Fusion and in other publications