  Tilings and point sets arising from substitutions are classical mathematical
models of quasicrystals. Their hierarchical structure allows one to obtain
concrete answers regarding spectral questions tied to the underlying measures
and potentials. In this review, we present some generalisations of
substitutions, with a focus on substitutions on compact alphabets, and with an
outlook towards their spectral theory. Guided by two main examples, we will
illustrate what changes when one moves from finite to compact (infinite)
alphabets, and discuss under which assumptions do we recover the usual
geometric and statistical properties which make them viable models of materials
with almost periodic order. We also present a planar example (which is a
two-dimensional generalisation of the Thue--Morse substitution), whose
diffraction is purely singular continuous.
