Next-generation wireless communications aim to utilize mmWave/subTHz bands. In this regime, signal propagation is vulnerable to interferences and path losses. To overcome this issue, a novel technology has been introduced, which is called reconfigurable intelligent surface (RIS). RISs control digitally the reflecting signals using many passive reflector arrays and implement a smart and modifiable radio environment for wireless communications. Nonetheless, channel estimation is the main problem of RIS-assisted systems because of their direct dependence on the system architecture design, the transmission channel configuration and methods used to compute channel state information (CSI) on a base station (BS) and RIS. In this paper, a concise survey on the up-to-date RIS-assisted wireless communications is provided and includes the massive multiple input-multiple output (mMIMO), multiple input-single output (MISO) and cell-free systems with an emphasis on effective algorithms computing CSI. In addition, we will present the effectiveness of the algorithms computing CSI for different communication systems and their techniques, and we will represent the most important ones.