The majority of thermonuclear explosions in the Universe seem to proceed in a rather standardised way, as explosions of carbon-oxygen (CO) white dwarfs in binary systems, leading to 'normal' Type Ia supernovae (SNe Ia). However, over the years a number of objects have been found which deviate from normal SNe Ia in their observational properties, and which require different and not seldom more extreme progenitor systems. While the 'traditional' classes of peculiar SNe Ia -luminous '91T-like' and faint '91bg-like' objects -have been known since the early 1990s, other classes of even more unusual transients have only been established 20 years later, fostered by the advent of new wide-field SN surveys such as the Palomar Transient Factory. These include the faint but slowly declining '02es-like' SNe, 'Ca-rich' transients residing in the luminosity gap between classical novae and supernovae, extremely short-lived, fast-declining transients, and the very luminous so-called 'super-Chandrasekhar' SNe Ia. Not all of them are necessarily thermonuclear explosions, but there are good arguments in favour of a thermonuclear origin for most of them. The aim of this chapter is to provide an overview of the zoo of potentially thermonuclear transients, reviewing their observational characteristics and discussing possible explosion scenarios.