Wide-field Herschel surveys have proved invaluable for identifying strongly gravitationally lensed dusty star-forming galaxies (DSFGs) at z~1-4. DSFGs are the most extreme starbursts in the Universe, with star-formation rates >~1000 solar masses per year, though the mode of star-formation and their triggering mechanisms are unclear. By targeting lensed DSFGs, magnified by factors of ~2-20, we are able to detect of photometric and spectroscopic features and unprecedented spatial resolutions. I will summarise the key insights into DSFGs that our lensing follow-up programs have produced, including a mid-infrared spectroscopic survey with Herschel/PACS that probes the conditions in the ISM of these extreme starbursts. Without the lensing amplification such observations would be impossible, and since the planned warm-up of Herschel, such spectroscopy will not again be attainable until the launch of facilities such as SPICA or the Far-Infrared Surveyor. I will present spectroscopy covering seven fine-structure transitions, including [OI]63um, [SiII]34um, and [OIV]26um in 13 lensed H-ATLAS and HerMES galaxies, and supplement that data with archival observations of a further 32 DSFGs. PDR modelling of the line ratios in the whole sample, supplemented with published [CII]158um data, is used to determine the gas density and radiation field strength in DSFGs, which is an indicator of the mode of star-formation.