The fifth generation (5G) mobile communication systems employ technologies such as massive MIMO, millimeter-wave (mmWave), and ultra-dense networks to support higher transmission data rate and lower latency, thereby enabling commercial deployment. Furthermore, the forthcoming sixth generation (6G) networks will integrate terrestrial and non-terrestrial networks, aiming to achieve full spectrum, full applications, and global coverage. Whether in the context of 5G or 6G networks, base transceiver stations (BTS) require a substantial number of radio frequency (RF) transceiver chains and antenna array, particularly in mmWave frequency bands. It is known that bandpass RF filters between antenna elements and transceivers are key components for suppressing out-of-band spurs and interference. The single board seamless integration of transceivers and antennas has become a growing trend. It means there is no extra room for a large number of filters at mmWave bands, leading to the emergence of integrated designs that combine filtering circuitry with antennas, known as filtenna or filtering antenna. With illustrated examples, the design methodologies, operational principles, and implementation strategies of filtennas are reviewed in this paper.