This survey reviews more than 50 papers concerning the mathematical study of information dissemination processes. Emphasis is given to the study of two of these processes, called gossiping and broadcasting. In gossiping, each person in a group has a unique item of informa­tion and must transmit it to everyone else. Thus gossip­ing is an all-to-all process. In broadcasting, only one person has an item of information which must be transmitted to everyone. Broadcasting is thus a one-to-all process.