This thesis is aimed to understand the physical properties of a new type of violent explosions , which have been labelled super-luminous supernovae (SLSNe). These SLSNe are 10 to 100 times brighter than normal SNe. However, the standard paradigm of iron-core collapse cannot account for the origin of these events and the mechanism which powers such luminosities is still not well established. We have used the all -sky survey telescope (e.g. Pan-STARRS1) to identify super-luminous transients, and triggered a global observational network for follow-up observations. The facilities include 8-m Gemini telescopes, 4-m William Herschel Tele- scope, New Technology Telescope (PESSTO) and other 1 to 2-m telescopes. Deep images were collected in the SN late-time phases, which is essential to examine alternative lightcurve models and to distinguish potential energy sources. One crucial strategy is to study the host galaxies of SLSNe Ic, which provide a strong constrain to understand the stellar progenitors of SLSNe Ic, e.g. metallicity. The most reliable method to quantitatively determine oxygen abundances needed for the metallicity measurement, without calibration uncertainties is the "direct method" which requires the electron temperature to be estimated from the auroral [0III] λ4363 line. We presented SLSN hosts that to be low metallicity dwarfs: the host of SN 2010gx is the lowest metallicity host of any type of SNe ever discovered, with an oxygen abundance of 1/20 of the solar value. The hosts of PTF12dam, SN 2011 ke, SN 2012il and LSQ14an, they also follow this low-metallicity trend. We therefore propose that there appears to be a metallicity threshold, and the formation of SLSNe only occurs below 12 + log(O/H) = 8.10 (direct method). The low-metallicity environment is favourable for both the magnetar scenario (as massive stars rotating more rapidly) as well as pair-instability models.