Foreign Member of the National Georgian Academy of Sciences.
Fellow of Royal Society of New Zealand,
Fellow of the Institute of Mathematical Statistics (IMS is the US-based professional society in probability theory and mathematical statistics, the biggest and, perhaps, the oldest).
Biography in Wikipedia, short biography in Springer’s Encyclopaedia of Statistics,                 
"Khmaladze transformation" in Wikipedia.
Name in the list of “Notable Statisticians’ in Wikipedia.

Contributions to statistics:

New connections between empirical processes and theory of semi-martingales;
Theory of sequential ranks;
Martingales in multi-dimensional time;
New notion of derivatives of set-valued functions and infinitesimal image analysis;
Theory of fragmentation processes, and statistical theory of diversity;
Theory of distribution free testing of statistical hypothesis