Jordan operator algebras

A survey of recent results in classification of $JW$-algebras (weakly closed Jordan algebras of self-adjoint operators in the Hilbert space) is given along with connections of $JW$-algebras with their enveloping $W^*$-algebras. It is shown how these results are applied in the proofs of analogs of many important results in the theory of $W^*$-algebras.