A non-comprehensive review of several technical developments in the field of aerobic biological waste-water treatment engineering is camed out, eonsidering the active role the engineers have to play in this field. This paper brings together conventional and advanced problems in the field of aerobic biological waste-water treatment. Such an overview of biological waste-water treatment also precedes comments on some important aspects concerning the microorganisms responsible for waste-water treatment as well as considerations of the application of fundamentals and kinetics to the analysis of the biological processes used most commonly for aerobic biological waste-water treatment.A survey of the development of the biological activated-sludge process and some modifications are given. Some problems implied in the conventional activated-sludge waste-water treatment are analyzed, considering conventional processes and bioreactor models (the continuous stirred-tank reactor model and the plug-flow reactor models of the activated-sludge process) as well as aerated lagoons. Further, modifications of the activated-sludge process are presented. These include additional details on the bioreactor progress and applications. with emphasis on aspects concerning airlift bioreactors and their variants, deep-shaft bioreactors and reciprocating jet bioreactors which are considered as the third generation of bioreactors owing to their important advantages in design, operation and performance in waste-water treatment. Sequencing-batch reactors and aerobic digestion processes, including conventional aerobic digestion, high-purity oxygen digestion, thermophilic aerobic digestion and cryophylic aerobic digestion are also reviewed. Finally, some aspects regarding the operational factors that are involved in the selection of the reactor type are included.