1. A process of making the cell-binding agent maytansinoid conjugate, the process comprising: (a) providing the cell-binding agent (b) modifying the cell-binding agent with a cross-linking agent, and (c) conjugating the modified cell-binding agent with a maytansinoid or a thiol-containing maytansinoid thereby providing the non-cleavable linker between the cell-binding agent and the maytansinoid or thiol-containing maytansinoid to produce the conjugate said cell-binding agent maytansinoid conjugate having at least one maytansinoid linked to a cell-binding agent via a non-cleavable linker, provided that when the cell-binding agent is an antibody, the linker is not derived from a crosslinking agent selected from the group consisting of: succinimidyl 4-(N-maleimidomethyl)-cyclohexane-1-carboxylate (SMCC), sulfo-SMCC, m-maleimidobenzoyl-N-hydroxysuccinimide ester (MBS), sulfo-MBS, and N-succinimidyl-iodoacetate (SIA), or said cell-binding agent maytansinoid conjugate having at least one maytansinoid linked to a cell-binding agent via a non-cleavable linker, provided that the cell-binding agent is not an antibody.