  The ever-growing appearance of infinitely divisible laws and related
processes in various areas, such as physics, mathematical biology, finance and
economics, has fuelled an increasing demand for numerical methods of sampling
and sample path generation. In this survey, we review shot noise representation
with a view towards sampling infinitely divisible laws and generating sample
paths of related processes. In contrast to many conventional methods, the shot
noise approach remains practical even in the multidimensional setting. We
provide a brief introduction to shot noise representations of infinitely
divisible laws and related processes, and discuss the truncation of such series
representations towards the simulation of infinitely divisible random vectors,
L\'evy processes, infinitely divisible processes and fields and L\'evy-driven
stochastic differential equations. Essential notions and results towards
practical implementation are outlined, and summaries of simulation recipes are
provided throughout along with numerical illustrations. Some future research
directions are highlighted.
