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tokens: possible powering source could be the spin-down of a magnetar (Kasen Bildsten 2010 ; Inserra et al. 2013 ; Nicholl et al. 2013 ). Another possibility is the interaction between the ejecta and an H-poor CSM (Chatzopoulos, Wheeler Vinko 2012 ; Sorokina et al. 2016 ; Vreeswijk et al. 2017 ). A third scenario could be a pulsational pair-instability SN (Woosley, Blinnikov Heger 2007 ; Woosley 2017 ), or pair-instability explosion of a very massive star (with a core of ≥50 M ⊙ , e.g. Gal-Yam et al. 2009 ; Dessart et al. 2013 ). The latter is perhaps limited only to slowly declining H-poor SLSNe, SLSNe-R, with a declining rate consistent with the radioactive decay of 56 Ni and 56 Co. Until recently, models predicted a long rise in contradiction to observations (Chen et al. 2015b ), but Kozyreva et al. ( 2017 ) showed that they can also be fast rising. The long rise times predicted by pair-instability supernova models have been seen in at least one SLSN (Lunnan et al. 2016 ). However, spectroscopic models predict spectra that are different from observations (Jerkstrand, Smartt Heger 2016 ). SLSNe-R are a potential subclass of SLSNe-I. The existence and characterization of this class is discussed in Gal-Yam ( 2012 ) and De Cia et al. (in preparation). While the debate on the powering source of SLSN-I is ongoing, the general agreement is that these explosions are associated with the death of massive stars, given their total radiated energies ( E > 10 51 erg, Gal-Yam 2012 ). The study of their host galaxies has revealed that SLSN-I require extreme hosts, e.g. with low-metallicity ( Z ≤ 0.5 Z ⊙ ) and a high rate of star formation (SFR) for their low mass (Neill et al. 2011 ; Lunnan et al. 2014 ; Thöne et al. 2015 ; Chen et al. 2016 ; Perley et al. 2016 ; Schulze et al. 2016 ), and strong emission lines (Leloudas et al. 2015 ). However, Perley et al. ( 2016 ) argue that a high rate of star formation is not required, since there are many counterexamples of SLSNe with low SFRs, based on slit spectroscopy. High-resolution observations with Hubble Space Telescope (HST) showed that the host galaxies of hydrogen-poor SLSNe are usually irregular dwarf galaxies with asymmetric morphology or multiple peaks (Lunnan et al. 2015 ; Angus et al. 2016 ). Gamma-ray bursts (GRBs) are another energetic phenomenon likely associated with deaths of massive stars (Hjorth et al. 2003 ). Their host galaxies show similarities to the hosts of SLSNe (Lunnan et al. 2014 ), although the latter are more extreme (Vreeswijk et al. 2014 ; Leloudas et al. 2015 ; Perley et al. 2016 ; Schulze et al. 2016 ). Fruchter et al. ( 2006 ) and Blanchard, Berger Fong ( 2016 ) showed that GRBs are more concentrated in the brightest regions of their host galaxies. Similarly, if SLSNe are indeed associated with very massive stars, and their hosts are unusual for the young stellar content (Leloudas et al. 2015 ; Thöne et al. 2015 ), one natural expectation is that they may explode in blue, UV bright,