ONE OF THE MOST IMPORTANT ANTICIPATED SOURCES FOR THE LOW-FREQUENCY SPACE-BASED GRAVITATIONAL-WAVE (GW) ANTENNA LISA ARE THE INSPIRALS OF STELLAR MASS COMPACT BODIES INTO MASSIVE BLACK HOLES. IN SUCH BINARIES THE SMALLER MEMBER SPENDS MANY TENS OF THOUSANDS OF ORBITS DEEP IN THE LARGER BLACK HOLE'S STRONG FIELD. AS SUCH GWS FROM THESE "EXTREME MASS RATIO INSPIRALS" (OR "EMRIS") CARRY A CLEAN MAP OF THE LARGE BLACK HOLE'S SPACETIME. PRELIMINARY ANALYSES SHOW THAT THESE SOURCES WILL MAKE POSSIBLE EXQUISITELY PRECISE MEASUREMENTS OF MASSIVE BLACK HOLE PROPERTIES MEASURING BLACK HOLE DEMOGRAPHICS TO REDSHIFT Z OF ABOUT 0.5 - 1 AND ENABLING PRECISE CONSISTENCY TESTS OF STRONG-FIELD GRAVITY NEAR BLACK HOLE EVENT HORIZONS. SUCH MEASUREMENTS WILL RELY HEAVILY ON THEORETICAL MODELING. EMRI WAVEFORMS WILL HAVE AMPLITUDES A FACTOR TEN OR MORE SMALLER THAN NOISE SO DETECTING AND MEASURING THEIR WAVES WILL REQUIRE MODELS THAT CAN TRACK EMRI WAVES' PHASE OVER THE TENS OF THOUSANDS OF ORBITS THAT THEY RADIATE IN THE BAND OF LISA. THEORETICAL EFFORTS OVER THE PAST DECADE HAVE DONE MUCH TO CLARIFY HOW WELL LISA CAN MEASURE THESE WAVES AND WHAT CAN BE LEARNED FROM GW MEASUREMENTS. MOST OF THE COMMUNITY'S EFFORTS ARE PRESENTLY FOCUSED ON SELF FORCE CALCULATIONS COMPUTING EFFECTS ARISING FROM THE COMPACT BODY'S INTERACTION WITH ITS OWN DEFORMATION TO THE SPACETIME. HOW FAR MUST SUCH ANALYSES BE PUSHED BEFORE WE ARE CONFIDENT WE HAVE MODELED ALL OBSERVATIONALLY SIGNIFICANT EFFECTS? IS SECOND ORDER IN THE SMALL BODY'S MASS RATIO "FAR ENOUGH"? WHAT OTHER EFFECTS MUST BE INCLUDED IN ORDER FOR EMRI MEASUREMENTS TO ACHIEVE THEIR PROMISE? DO WE NEED TO INCLUDE THE INFLUENCE OF THE SMALLER BODY'S SPIN OR ITS QUADRUPOLE MOMENT? CAN A THIRD BODY IN THE NEIGHBORHOOD OF THE EMRI AFFECT THE SYSTEM AT A SIGNIFICANT LEVEL? WE PROPOSE TO MAKE A SYSTEMATIC ANALYSIS OF WHAT EFFECTS CAN IMPACT AN EMRI SYSTEM'S EVOLUTION. WE PLAN TO CATALOG BOTH HOW FAR ANALYSES MUST BE TAKEN AND WHAT EFFECTS MUST BE INCLUDED IN ORDER FOR EMRI MEASUREMENTS TO LIVE UP TO THEIR PROMISE.