Several aspects of quantum integrability related to Yangian symmetry are discussed. The orthosymplectic super-Yangian Y(osp(mjn)) and its finite order evaluations are investigated. The finite order evaluations imply the characteristic conditions of the polynomial type constraining representations of the orthosymplectic Lie superalgebra osp(mjn). The superspinorial, Jordan-Schwinger, and fundamental representations and the corresponding characteristic identities are discussed. They are consequently identified with the linear and quadratic evaluation of the super-Yangian. An R-operator in the superspinorial representation is constructed and its relation to the finite order evaluations is discussed. The form factors of local operators in integrable models based on the super-Yangians Y(gl(2j1)) and Y(gl(1j2)) are investigated. The method is based on the composite model and zero modes. An explicit representation for Bethe vectors in terms of the composite model is found and used to calculate form
factors of partial zero modes and the form factors of local operators. The form factors of local operators are proportional to the universal form factors. Symmetric correlators for the Yangian Y(sl(2)) are discussed. The explicit examples and their construction in several representations are provided. The q-deformation of symmetric correlators is discussed. The symmetric correlators are used as kernels of integral operators. The
properties and Yang-Baxter relations for the integral operators are investigated. The spectral problem for the generalized R-operator is solved.