One of the fundamental assumptions made in the design of wireless networks is that the wireless devices have to be half-duplex, i.e., they cannot simultaneously transmit and receive in the same frequency band. The key deterrent in implementing a full-duplex wireless device, which can simultaneously transmit and receive in the same frequency band, is the large power differential between the self-interference from a device's own transmissions and the signal of interest coming from a distant source. In this thesis, we revisit this basic assumption and propose a full-duplex radio design. The design suppresses the self-interference signal by employing a combination of passive suppression, and active analog and digital cancellation mechanisms. The active cancellations are designed for wideband, multiple subcarrier (OFDM), and multiple antenna (MIMO) wireless communications systems. We then implement our design as a 20 MHz MIMO OFDM system with a 2.4 GHz center frequency, suitable for Wi-Fi systems. We perform extensive over-the-air tests to characterize our implementation. Our main contributions are the following: (a) the average amount of active cancellation increases as the received self-interference power increases and as a result, the rate of a full-duplex link increases as the transmit power of communicating devices increases, (b) applying digital cancellation after analog cancellation can sometimes increase the self-interference and the effectiveness of digital cancellation in a full-duplex system will depend on the performance of the cancellation stages that precede it, (c) our full-duplex device design achieves an average of 85 dB of self-interference cancellation over a 20 MHz bandwidth at 2.4 GHz, which is the best cancellation performance reported to date, (d) our full-duplex device design achieves 30-84% higher ergodic rates than its half-duplex counterpart for received powers in the range of [-75, -60] dBm. As a result, our design is the first one to achieve Wi-Fi ranges; in comparison, no implementation to date has achieved Wi-Fi ranges. Consequently, we have conclusively demonstrated that Wi-Fi full-duplex is practically feasible and hence shown that one of the commonly made assumptions in wireless networks is not fundamental.