Passengers arriving at a bus stop at a random time may on average wait longer than the mean time between bus arrivals. This is a counter-intuitive result, since one expects to wait less when coming some time after the previous bus departed. In this talk, I will review the origins of this phenomenon, a.k.a. the inspection paradox, and use the lessons learned to explain why, and under which conditions, stochastic resetting expedites the completion of random processes: from diffusion, via enzymatic reactions, and on to realistic versions of stochastic search and animal foraging. To this end, I will (re)derive a series of central results that appeared in the literature using nothing but elementary mathematical tools—emphasizing the strength of the approach and the deep probabilistic insight it provides on stochastic resetting and how it works.