Ever since the birth of the telephony system, the problem with echoes, arising from impedance mismatch in 2/4-wire hybrids, or acoustic echoes where a loudspeaker signal is picked up by a closely located microphone, has been ever present. The removal of these echoes is crucial in order to achieve an acceptable audio quality for conversation. Today, the perhaps most common way for echo removal is through cancellation, where an adaptive filter is used to produce an estimated replica of the echo which is then subtracted from the echo-infested signal. Echo cancellation in practice requires extensive control of the filter adaptation process in order to obtain as rapid convergence as possible while also achieving robustness towards disturbances. Moreover, despite the rapid advancement in the computational capabilities of modern digital signal processors there is a constant demand for low-complexity solutions that can be implemented using low power and low cost hardware. This thesis presents low-complexity solutions for echo cancellation related to both the actual filter adaptation process itself as well as for controlling the adaptation process in order to obtain a robust system. Extensive simulations and evaluations using real world recorded signals are used to demonstrate the performance of the proposed solutions.