The spectral region between 1250-3000 Å contains important spectral lines to understand the morphological structures and evolution of planetary nebulae. This is the region sampled by UVIT through various filter bands both in the continuum and in emission lines (e.g.. [C IV], [He I], [Mg II] etc.). We have mapped several planetary nebulae with different characteristics, ranging in morphology from bipolar to wide and diffuse, and in various states of ionization, comparing the UV with the X-ray morphologies wherever the X-ray images were also available. The major unanticipated discovery with UVIT has been the detection of previously undetected, cold, fluorescent, H2 gas surrounding some planetary nebulae. This may be a possible solution to the missing mass problem. Here we present a review of our studies so far done (both published and on going) with UVIT.