  Over the past several years, there has been enormous interest in massive
neutron stars and white dwarfs due to either their direct or indirect evidence.
The recent detection of gravitational wave event GW190814 has confirmed the
existence of compact stars with masses as high as $\sim2.5-2.67M_{\odot}$
within the so-called mass gap, indicating the existence of highly massive
neutron stars. One of the primary goals to invoke massive compact objects was
to explain the recent detections of over a dozen Type Ia supernovae, whose
peculiarity lies with their unusual light curve, in particular the high
luminosity and low ejecta velocity. In a series of recent papers, our group has
proposed that highly magnetised white dwarfs with super-Chandrasekhar masses
can be promising candidates for the progenitors of these peculiar supernovae.
The mass-radius relations of these magnetised stars are significantly different
from those of their non-magnetised counterparts, which leads to a revised
super-Chandrasekhar mass-limit. These compact stars have wider ranging
implications, including those for soft gamma-ray repeaters, anomalous X-ray
pulsars, white dwarf pulsars and gravitational radiation. Here we review the
development of the subject over the last decade or so, describing the overall
state of the art of the subject as it stands now. We mainly touch upon the
possible formation channels of these intriguing stars as well as the
effectiveness of direct detection methods. These magnetised stars can have many
interesting consequences, including reconsideration of them as possible
standard candles.
