The freeze-in picture is a well-established alternative to thermal freeze-out that can explain the dark matter abundance in the Universe. Typical frozen-in dark matter candidates are characterised by tiny couplings to the visible sector, which can be hard to justify from a particle physics standpoint. I will discuss potential ways to address this issue, focusing on the possibility that these couplings could be suppressed due to the so-called Clockwork mechanism. I will present two main variants of this idea, one for scalar and one for fermionic dark matter. Finally, time permitting, I will also discuss some interesting signatures that freeze-in models could have at the Large Hadron Collider.