  We present a review on the notion of pure states and mixtures as mathematical
concepts that apply for both classical and quantum physical theories, as well
as for any other theory depending on statistical description. Here, states will
be presented as expectation values on suitable algebras of observables, in a
manner intended for the non-specialist reader; accordingly, basic literature on
the subject will be provided. Examples will be exposed together with a
discussion on their meanings and implications. An example will be shown where a
pure quantum state converges to a classical mixture of particles as Planck's
constant tends to zero.
