The aphid Myzus persicae s.l. (Hemiptera: Aphididae) is an important pest of many crops worldwide with a complex life cycle, intensely controlled by chemical pesticides, and has developed resistance to almost all used insecticides. In Greece, the aphid exhibits high genetic variation and adaptability and it is a classic example of evolution in the making. We have been studying M. persicae for over 20 years, on different host plants and varying geographical areas, analyzing its bio-ecology and the ability to develop resistance to insecticides. In this review, we present new and historical data on the effectiveness of insecticides from seven chemical groups used to control the aphid in Greece and the incidence of seven resistance mechanisms, including the new fast-spreading R81T point mutation of the postsynaptic nicotinic acetylcholine receptor. Thousands of samples were tested by biological, biochemical and molecular assays. The aphid populations were found to have developed and maintain resistance at medium to high levels to organophosphates, carbamates, pyrethroids and neonicotinoids for decades. In the latter group, a marked increase is recorded during an ~10-year period. The data analyzed and the extensive bibliography, advocate the difficulty to control the aphid making the design and application of IPM/IRM programs a challenge. We discuss principles and recommendations for the management of resistance, including the use of compounds such as flonicamid, spirotetramat, flupyradifurone and sulfoxaflor. We emphasize that resistance is a dynamic phenomenon, changing in time and space, requiring, therefore, continuous monitoring.