WE PROPOSE TWO RELATED PROJECTS TO EXPLORE DUST TRANSPORT AND EVOLUTION IN THE INTERSTELLAR MEDIUM (ISM) IN GALAXIES ON BOTH SMALL SCALES AND LARGE SCALES. FIRST WE WILL IMPROVE THE MODELING OF THE ESCAPE OF SUPERNOVA-CREATED DUST GRAINS FROM THEIR NATAL EJECTA CLUMPS AND OUT OF THE HOT INTERIOR OF THE SUPERNOVA REMNANT. THAT PROJECT WILL AIM TO DETERMINE HOW MUCH DUST CAN BE INJECTED INTO THE ISM BY PRIMORDIAL AND MODERN SUPERNOVAE. SECOND WE WILL MODEL THE SUBSEQUENT TRANSPORT AND PROCESSING OF DUST GRAINS FROM THEIR BIRTHPLACES IN SUPERNOVAE OR ASYMPTOTIC GIANT BRANCH STARS UNTIL THEY ARE DESTROYED. THAT PROJECT WILL HAVE AS ITS GOAL UNDERSTANDING HOW THE OBSERVED SIZE DISTRIBUTION ABUNDANCE AND LIFETIME OF GRAINS ARE DETERMINED BY PROCESSES OCCURRING THROUGHOUT THE ISM MOVING BEYOND GLOBAL AVERAGING TO EXAMINE THE RANGE OF OUTCOMES THAT OCCUR FOR INDIVIDUAL GRAINS. AS PART OF THE SECOND PROJECT WE WILL EXAMINE WHETHER GRAIN PROCESSING YIELDS DIFFERENT DEPLETION LEVELS IN MILKY WAY-TYPE GALAXIES COMPARED TO LOW-METALLICITY DWARF GALAXIES. THESE PROJECTS WILL INVOLVE THE USE PRE-EXISTING NUMERICAL HYDRODYNAMICAL CODES IN CONCERT WITH OUR DUST PROCESSING CODES. THE RESULTS OF OUR WORK WILL AID IN UNDERSTANDING A WIDE RANGE OF OBSERVATIONS CARRIED OUT BY NASA MISSIONS RANGING FROM INFRARED EMISSION GENERATED BY HEATED DUST TO ELEMENTAL DEPLETION PATTERNS DEDUCED VIA UV OBSERVATIONS AND X-RAY EMISSION FROM SUPERNOVA REMNANTS. DUST PLAYS A CRITICAL ROLE GALAXY EVOLUTION AND SO OUR RESULTS WILL ALSO AID IN A BROAD RANGE OF INVESTIGATIONS RELATED TO STAR FORMATION AND METALLICITY EVOLUTION FROM GALAXIES IN THE EARLY UNIVERSE UP UNTIL THE CURRENT EPOCH.