  Coideal subalgebras of the quantized enveloping algebra are surveyed, with
selected proofs included. The first half of the paper studies generators,
Harish-Chandra modules, and associated quantum homogeneous spaces. The second
half discusses various well known quantum coideal subalgebras and the
implications of the abstract theory on these examples. The focus is on the
locally finite part of the quantized enveloping algebra, analogs of enveloping
algebras of nilpotent Lie subalgebras, and coideals used to form quantum
symmetric pairs. The last family of examples is explored in detail. Connections
are made to the construction of quantum symmetric spaces.
