Precoding has been conventionally considered as an effective means of mitigating the interference and efficiently exploiting the available in the multiantenna downlink channel, where multiple users are simultaneously served with independent information over the same channel resources. The early works in this area were focused on transmitting an individual information stream to each user by constructing weighted linear combinations of symbol blocks (codewords). However, more recent works have moved beyond this traditional view by: i) transmitting distinct data streams to groups of users and ii) applying precoding on a symbol-per-symbol basis. In this context, the current survey presents a unified view and classification of precoding techniques with respect to two main axes: i) the switching rate of the precoding weights, leading to the classes of block- and symbol-level precoding, ii) the number of users that each stream is addressed to, hence unicast-/multicast-/broadcast- precoding. Furthermore, the classified techniques are compared through representative numerical results to demonstrate their relative performance and uncover fundamental insights. Finally, a list of open theoretical problems and practical challenges are presented to inspire further research in this area.