The idea of immunological memory originally arose from the observation that survivors of infections were subsequently resistant to disease caused by the same infection. While most immunologists accept a special 'remembering' memory quality, we have argued previously and document here that increased resistance against re-infection, i.e. immunity, reflects low-level antigen-driven T- and B-cell responses, resulting in elevated serum or mucosal titers of protective antibodies or of activated T cells, respectively. Periodic antigen re-exposure is from within, by persisting infection (long-term) or by immune complexes (short-term), or from without, by low-level re-infections. This simple concept is supported by clinical evidence and model experiments but is often ignored, although this concept, but not so-called 'immunological memory', as defined in textbooks (i.e. earlier and better responses of a primed host), is compatible with evolutionary maternal antibody transfer of protection as well as immunity against existing infections. The concept of 'immunity without immunological remembering memory' explains why it is easy to generate vaccines against acute cytopathic infections, particularly those of early childhood, where neutralizing antibodies are the key to protection, because it has been validated by adoptive transfer of maternal antibodies. It also explains why we have not succeeded (yet?) to generate truly protective vaccines against persisting infections, because we cannot imitate 'infection immunity' that is long-lasting, generating protective T- and B-cell stimulation against variable infections without causing disease by either immunopathology or tolerance.