This chapter deals with the formation and interactions of matter-wave solitons in one- and two-component Bose-Einstein condensates. Applying the method of the linear stability analysis, we investigateBose-Einstein condensate the modulational instability phenomenon thatModulational instability predicts the formation of matter wave solitons in coupled Bose-Einstein condensates whose dynamics are governed by the Gross-Pitaevskii equations with external potentials. Based on analytical exact solutions of the model equations (coupled Gross-Pitaevskii equations), we then investigate analytically the solitons interactions in such Bose-Einstein condensates.Bose-Einstein condensate