  We give a complete description of the finite-dimensional irreducible
representations of the Yangian associated with the orthosymplectic Lie
superalgebra $\frak{osp}_{1|2}$. The representations are parameterized by monic
polynomials in one variable, they are classified in terms of highest weights.
We give explicit constructions of a family of elementary modules of the Yangian
and show that a wide class of irreducible representations can be produced by
taking tensor products of the elementary modules.
