  We find the general form of all the supersymmetric configurations and
solutions of N=2,d=4 Einstein-Yang-Mills theories. In the timelike case, which
we study in great detail, giving many examples, the solutions to the full
supergravity equations can be constructed from known flat spacetime solutions
of the Bogomol'nyi equations. This allows the regular supersymmetric embedding
in supergravity of regular monopole solutions ('t Hooft-Poyakov's, Weinberg's,
Wilkinson and Bais's) but also embeddings of irregular solutions to the
Bogomol'nyi equations which turn out to be regular black holes with different
forms of non-Abelian hair once the non-triviality of the spacetime metric is
taken into account. The attractor mechanism is realized in a gauge-covariant
way. In the null case we determine the general equations that supersymmetric
configurations and solutions must satisfy but we do not find relevant new
supersymmetric solutions.
