The configuration-interaction (CI) method is used to investigate the interactions of positrons and positronium with copper at low energies. The calculations were performed within the framework of the fixed-core approximation with semiempirical polarization potentials used to model dynamical interactions between the active particles and the (1s-3d) core. Initially, calculations upon the e(+)Li system were used to refine the numerical procedures and highlighted the extreme difficulties of using an orthodox CI calculation to describe the e(+)Li system. The positron binding energy of e(+) Cu derived from a CI calculation which included electron and positron orbitals with l less than or equal to 18 was. 0.005 12 hartree while the spin-averaged annihilation rate was 0.507 x 10(9) s(-1). The configuration basis used for the bound-state calculation was also used as a part of the trial wave function for a Kohn variational calculation of positron-copper scattering. The positron-copper system has a scattering length of about 13.1a(0) and the annihilation parameter Z(eff) at threshold was 72.9. The dipole polarizability of the neutral copper ground state was computed and found to be 41.6a(0)(3). The structure of CuPs was also studied with the CI method and it was found to have a binding energy of 0.0143 hartree and an annihilation rate of similar to2 x 10(9) s(-1).