In this paper we compare linear and non-linear interference cancellation for systems employing code division multiple access (CDMA) techniques. Specifically, we examine linear and non-linear parallel interference cancellation (also called multistage cancellation) in relationship to other multiuser detection algorithms. We show the explicit relationship between parallel interference cancellation and the decorrelator (or direct matrix inversion). This comparison gives insight into the performance of parallel interference cancellation (PIC) and leads to better approaches. We also show that non-linear PIC approaches with explicit channel estimation can provide performance improvement over linear PIC, especially when using soft non-linear symbol estimates. The application of interference cancellation to non-linear modulation techniques is also presented along with a discussion on minimum mean-squared error (MMSE) symbol estimation techniques. These are shown to further improve the performance of parallel cancellation.