Here we report and discuss the strategy of using the study of present ultra-short laser pulses to develop a better understanding of wavepackets and their propagation. It is well-known that in spite of its relevance and ubiquity this subject does not receive in modern optics courses the extra attention it deserves, very much in the same way that it happens in introductory physics courses or even in quantum mechanics courses. Notwithstanding, the subject has become very important both in applied optics and quantum optics, in multiple ways. For instance the generation and applications of femtosecond laser pulses, the exploitation of laser pulses as a tool in quantum control, the propagation of solitons in optical fibers, or even the propagation of light pulses in rather special media such as a Bose-Einstein condensate. A set of cases taken from applications in ultrashort laser pulse optics, non-linear optics, and optics communications, can be used to present wavepackets physics and the associated transform calculus related to the models involved. The set of cases can be also illustrated with simulations in which optical phase is seen to play the crucial role. A comparison with the traditional way of teaching wavepackets is presented.