We study Red Misfits, a population of red, star-forming galaxies in the local Universe. We classify galaxies based on inclination-corrected optical colours and specific star formation rates derived from the Sloan Digital Sky Survey Data Release 7. Although the majority of blue galaxies are star-forming and most red galaxies exhibit little to no ongoing star formation, a small but significant population of galaxies ($\sim$11 per cent at all stellar masses) are classified as red in colour yet actively star-forming. We explore a number of properties of these galaxies and demonstrate that Red Misfits are not simply dusty or highly-inclined blue cloud galaxies or quiescent red galaxies with poorly-constrained star formation. The proportion of Red Misfits is nearly independent of environment and this population exhibits both intermediate morphologies and an enhanced likelihood of hosting an AGN. We conclude that Red Misfits are a transition population, gradually quenching on their way to the red sequence and this quenching is dominated by internal processes rather than environmentally-driven processes. We discuss the connection between Red Misfits and other transition galaxy populations, namely S0's, red spirals and green valley galaxies.