The past decade has seen tremendous interest in mixed criticality systems research due to its exponential growth with inherent challenges of effective resource utilisation and isolation. The pervasiveness of these systems along with their certification needs, prompt for suitable task models to perform the required analysis. Extensive usage scenarios and strict certification requirements have spawned a broad spectrum of research and evolved into several task models. In this work, a thematic survey of task models for both uni-core and multi-core mixed criticality systems is carried out. The work categorises task models based on attributes such as resources, quality of service, operating system overheads, energy, fault tolerance and parallel processing. After synthesising the state-of-the-art, the work summarises task models by providing a visual aid and a ready reckoner with traceability to mixed criticality challenges. This work serves as a quintessential reference manual for researchers and academicians in the mixed criticality domain.