© 2015 BIPM & IOP Publishing Ltd. Spectroscopy has been a key driver and motivator of new understanding at the heart of physics. Here we describe high-precision measurements of the absorption lineshape of an atomic gas with an aim towards primary thermometry. We describe our progress in pushing this type of spectroscopy to the ultimate limit, in particular in describing experimental work with Rubidium and Cesium, although we also consider the potential for other elements in expanding the precision, accuracy and range of the approach. We describe the important technical and theoretical limits which need to be overcome in order to obtain accurate and precise results-these challenges are not unique to atomic spectroscopy but are likely to afflict all high precision spectroscopy measurements. We obtain a value for kB = 1.380 545(98) × 10?23 J K?1 where the 71 ppm uncertainty arises with difficulties in defining the Lorentzian component of the lineshape.