Massive stars end their life as energetic supernova (SN) explosions. They are produced from a wide range of progenitor and environments, and so their observed properties are also diverse. Despite several decades of studies of these objects, various aspects are still poorly understood and highly debated. With the emergence of several all-sky and untargeted surveys, we are now able to find several extreme and unusual SNe which were previously unknown and challenges our present understanding of these objects. It is important to examine the rare and peculiar behaviors of these SNe to find clues to the missing links in our present understanding. I will discuss a few interesting and rare SNe which we studied, namely Gaia17biu, ASASSN-16at, and ASASSN-15nx. Gaia17biu belongs to a very luminous and rare class of supernovae, known as Superluminous supernovae (SLSNe). The SN was discovered in a host galaxy which is very unusual for these type of objects. Interestingly Gaia17biu was also the closest SLSN-I when discovered. We observed this SN in unprecedented detail, which was not possible for any other SLSNe. Another object, ASASSN-16at was a normal hydrogen-rich supernova as evident from early time evolution. However, the late nebular phase spectra showed strong bifurcation in HI emissions lines, which is unprecedented for any SNe. Such a double-peaked profile of HI emission suggests strong bipolarity in inner ejecta. The third object, ASASSN-15nx, is a peculiar hydrogen-rich supernova, with luminosity in between core-collapse and superluminous SNe. Among a host of peculiar features, ASASSN-15nx showed a remarkable, almost perfect linear-declining light-curve until 270 days. Such an atypical light curve evolution contradicts our present understanding of CCSNe. Although the exact powering mechanism is still unclear, from our detailed study, we proposed some of the possible scenarios to explain the observed behaviors.
