The present invention relates to novel Histone Deacetylase Inhibitors (HDACi)-based antibody drug conjugates with antibodies directed against a histone deacetylase inhibitor or against a receptor internalized by tumor cells to release a histone deacetylase inhibitor, particularly with antibodies directed to ErbB1, ErbB2 and ErbB3 receptors, pharmaceutical compositions comprising said antibodies as well as to their use in the treatment of cancer or tumor and other diseases where a modulation of one or more histone deacetylase isoforms can be effective for therapeutic interventions.