The maturation of B cells leads to the synthesis of highly evolved immunoglobulins (Igs) that enable efficient antigen-antibody recognition. Here we discuss a non-opportunistic, combinatorial concept of “maturation” of Igs in silico for the production of artificially-evolved immunocatalysts. Several recent breakthroughs including: (i) single B cell selection using microfluidic technology (ii) combinatorial approaches powered by library screening (iii) structural computing and machine learning, (iv) quantum mechanics/molecular mechanics (QM/MM) evaluations of catalytic reaction leading to optimistic prospect for the elaboration of more effective immunoglobulin-derived catalytic templates and redirection the selection process to a purely robotic procedure. The synergy of these approaches enable catalytic antibody become a great prospect for biomedical purposes. The most recent breakthroughs include therapeutic antibodies and catalytic Chimeric Antigen Receptors (catCARs) with controllable pharmacokinetic parameters.