Cortana plays a pivotal role in Halo 4. Her decent into rampancy will test the Chief in ways he's never faced.
Cortana has a more human appearance in The Reclaimer Trilogy. According to Frank O'Connor, "the fact that she's a beautiful blue naked lady is tactically designed to give her an advantage over people in conversations, because it's a little bit distracting".
Here's a series of pictures that charts the evolution of Cortana throughout the series.