We present an overview of a fully covariant formulation for describing the production of strangeness −1 and −2 hypernuclei using probes of different kinds. This theory is based on an effective Lagrangian picture and it focuses on production amplitudes that are described via creation, propagation and decay into relevant channel of intermediate baryonic resonance states in the initial collision of the projectile with one of the target nucleons. The bound state
nucleon and hyperon
wave functions are obtained by solving the Dirac equation with appropriate scalar and vector potentials. Specific examples are discussed for reactions which are of interest to current and future experiments on the hypernuclear production.