This thesis investigates techniques and algorithms for mitigating radio frequency interference (RFI) affecting radio astronomy observations. In the past radio astronomy has generally been performed in radio-quiet geographical locations and unused parts of the radio spectrum, including small protected frequency bands. The increasing use of the entire spectrum and global transmitters such as satellites are forcing the astronomy community to begin implementing active interference cancelling. The amount of harmful interference affecting observations will also increase as future instruments such as the Square Kilometre Array (SKA) are required to use larger bandwidths to reach up to 100 times the current sensitivity levels, and as spectral line observations require observing in bands licensed to other spectrum users. Particular attention is paid to interference cancellation algorithms which make use of reference beams. This has proven to be successful in removing interference from the contaminated astronomical data. Reference antenna cancellers are closely analysed, leading to filters and techniques that can offer improved RFI excision for some important applications. It is shown that pre- and post-correlation reference antenna cancellers give similar results, and an important aspect of the cancellers is the use of a second reference signal when the reference interference-to-noise ratio is low. These modified filters can theoretically offer infinite interference suppression in the voltage domain, equivalent to that of post-correlation interference cancellers, and their internal structure can offer an understanding of the residual RFI and added receiver noise components of a variety of reference antenna techniques. The effect of variable geometric delays is also considered and various filters are compared as a function of the geometric fringe rate.