The main research topic of HS has been to understand how alterations in cellular membrane dynamics promote cancer progression. A central contribution was his discovery of a conserved protein domain called the FYVE domain (Stenmark et al. Journal of Biological Chemistry,1996), which binds to the membrane lipid PI3P, the catalytic product of the tumour suppressor PIK3C3 (Gaullier et al., Nature, 1998). By identifying and characterizing a number of FYVE domain-containing PI3P binding proteins, HS and his co-workers have uncovered how PI3P recruits cytosolic proteins to specific intracellular membranes to control lysosomal degradation of growth factor receptors (Simonsen et al., Nature, 1998; Raiborg et al., Nature Cell Biology, 2002). This is important in order to understand the tumour suppressor function of PIK3C3 because lysosomal degradation of growth factors, mediated by the so-called ESCRT machinery, is a key mechanism to prevent overstimulation of cells by growth factors, a mechanism that is often inactivated in cancer (Raiborg and Stenmark, Nature, 2009). A further breakthrough was the identification of two PI3P-binding proteins that cooperate to control lysosome positioning and protrusion outgrowth, a topic of high relevance to cell signalling and cancer metastasis (Raiborg et al., Nature, 2015). The group of HS has also shown how PI3P-binding proteins regulate the final stage of cell division, cytokinesis, and demonstrated how their dysfunction can cause an abnormal number of chromosomes, a condition that promotes cancer development (Sagona et al., Nature Cell Biology, 2010; Thoresen et al., Nature Cell Biology, 2014). An important discovery was that the ESCRT machinery mediates sealing of the newly formed nuclear envelope during cell division, and that failure of this mechanism causes DNA damage, which is a driver of cancer progression (Vietri et al., Nature, 2015; received commentaries in both Nature and Science). This was followed up by a study showing that hyper-recruitment of ESCRT proteins to damaged micronuclei causes micronuclear catastrophe and chromosome damage (Vietri et al., Nature Cell Biology, 2020). Recently, the HS group co-discovered ESCRT-mediated mechanisms for repair of damaged lysosomes (Radulovic et al., 2018, EMBO Journal, 2018), and sealing of autophagosomes (Zhen et al., Autophagy, 2020).