We discuss the critical role that first order phase transitions in the early Universe may play in the production of dark matter. We describe a mechanism dubbed "Filtered Dark Matter", where it is assumed that dark matter particles acquire mass during the phase transition, making it energetically unfavourable for them to enter the expanding bubbles of the massive phase. Instead, most of them are reflected off the advancing bubble walls and quickly annihilate away in the massless phase. Only the dark matter particles which have entered the bubbles survive to constitute the observed dark matter today. Towards the end of the talk, we will also briefly mention other ways in which phase transitions can be crucial in determining the dark matter abundance, and we discuss how such scenarios can be probed experimentally.
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