  Private information retrieval (PIR) is a privacy setting that allows a user
to download a required message from a set of messages stored in a system of
databases without revealing the index of the required message to the databases.
PIR was introduced under computational privacy guarantees, and is recently
re-formulated to provide information-theoretic guarantees, resulting in
\emph{information theoretic privacy}. Subsequently, many important variants of
the basic PIR problem have been studied focusing on fundamental performance
limits as well as achievable schemes. More recently, a variety of conceptual
extensions of PIR have been introduced, such as, private set intersection
(PSI), private set union (PSU), and private read-update-write (PRUW). Some of
these extensions are mainly intended to solve the privacy issues that arise in
distributed learning applications due to the extensive dependency of machine
learning on users' private data. In this article, we first provide an
introduction to basic PIR with examples, followed by a brief description of its
immediate variants. We then provide a detailed discussion on the conceptual
extensions of PIR, along with potential research directions.
