This paper is a summary of our work on the relationship between under-compacted shale and abnormal pressure in the Tertiary portion of the Gulf of Mexico Basin. A major objective of this study is to map the depth to the top of the undercompacted shale, as located using shale density (cuttings samples), conductivity, sonic, plus bulk density logs relative to the depth to the top of abnormal pore pressure as determined using bottom-hole pressure (BHP) and repeat formation tester (RFT) data. Geopressure profiles (formation pressure versus depth curves) were most useful for such mapping because the geopressure profiles showed linear segments in which pressure gradients were constant. Although the top of abnormal pressure and the top of undercompaction sometimes occur at the same depth in a given field area, often these boundaries are separated by hundreds of feet (tens of meters) and in some cases by vertical distances of over 2000 ft (600 m). Two types of field areas in the Tertiary portion of the Gulf of Mexico are distinguished based on whether or not the top of undercompaction and the top of abnormal pressure correspond. Tertiary fields have geopressure profiles characterized by pressure gradients showing either three (the Alazan-type field) or four (the Ann Mag-type field) linear segments. One consequence of our work is that electropressure methods which assume that the top of abnormal pressure is always coincident with the top of the zone of undercompaction are unreliable when used for a quantitative estimate of geopressure.