  The most up to date femto- and micro-lensing constraints indicate that
primordial black holes of $\sim 10^{-16} M_\odot$ and $\sim 10^{-12} M_\odot$,
respectively, may constitute a large fraction of the dark matter. We describe
analytically and numerically the dynamics by which inflationary fluctuations
featuring a time-varying propagation speed or an effective Planck mass can lead
to abundant primordial black hole production. As an example, we provide an ad
hoc DBI-like model. A very large primordial spectrum originating from a small
speed of sound typically leads to strong coupling within the vanilla effective
theory of inflationary perturbations. However, we point out that ghost
inflation may be able to circumvent this problem. We consider as well black
hole formation in solid inflation, for which, in addition to an analogous
difficulty, we stress the importance of the reheating process. In addition, we
review the basic formalism for the collapse of large radiation density
fluctuations, emphasizing the relevance of an adequate choice of gauge
invariant variables.
