A conversation server system having one or more processors and memory stores a plurality of messages organized as a plurality of conversations, respective conversations including respective representative messages with message term(s) and conversation term(s) and messages with message term(s). The server receives a message search query and responds by: identifying matching message(s) associated with message terms matching the message search query; and returning message search results including representations matching message(s) to a client from which the message search query was received. The server also receives a conversation search query and responds by: identifying matching representative message(s) associated with a combination of message term(s) and conversation term(s) matching the conversation search query, selecting conversation(s) including a matching representative message; and returning conversation search results including representations of matching conversation(s) to a client from which the conversation search query was received.