With the globalization of the world’s economy, the demand for effortless, quick and efficient communication is increasing. Modern audio conferencing allows people at different locations to have a conversation as if they were sitting in the same room, without having to travel. This obviously saves time and money, and also lessens the environmental strain caused by travel. Most audio conferencing systems and hands-free systems in particular, suffer from electric and/or acoustic echoes. Electric echoes typically originate from 2-4 wire conversion in hybrid circuits in the telephone network, while acoustic echoes arise due to acoustic coupling between loudspeaker and microphone. In digital audio communication equipment, the echoes are usually removed through digital signal processing methods such as adaptive filtering. Since audio conferencing systems are consumer electronic products, the manufacturing cost is a key issue. In order to accomplish low manufacturing costs, the choice of a low cost digital signal processor (DSP) to perform the signal processing tasks is central. Further, due to the limited resources of low cost DSPs, there is an intrinsic demand for low complexity signal processing algorithms. This thesis presents low complexity algorithms for adaptive filtering in acoustic echo cancellation applications. Both the actual update of the adaptive filter and the update control to prevent divergence and so called howling, are considered. Computer simulations, as well as real time implementations in actual acoustic systems are used to verify the performance of the proposed algorithms.