In December 2012, Curiosity's two-year mission was extended indefinitely. On August 5, 2017, NASA celebrated the fifth anniversary of the Curiosity rover landing and related exploratory accomplishments on the planet Mars. The rover is still operational, and as of September 24, 2018, Curiosity has been on Mars for 2181 sols (2240 total days) since landing on August 6, 2012. (See current status.)
Curiosity's design will serve as the basis for the planned Mars 2020 rover.
About one year into the surface mission, and having assessed that ancient Mars could have been hospitable to microbial life, the MSL mission objectives evolved to developing predictive models for the preservation process of organic compounds and biomolecules; a branch of paleontology called taphonomy.