Problems of scientific cosmology only rarely occur in the works of Karl Popper. Nevertheless, it was a subject that interested him and which he occasionally commented on. What is more important, his general claim of falsifiability as a criterion that demarcates science from non-science has played a significant role in periods of the development of modern physical cosmology. The paper examines the historical contexts of the interaction between cosmology and Popperian philosophy of science. Apart from covering Popper's inspiration from Einstein and his views on questions of cosmology, it focuses on the impact of his thoughts in two periods of controversy of modern cosmology, the one related to the steady state theory and the other to the recent multiverse proposal. It turns out that the impact has been considerable, and continues to be so, but also that the versions of Popperian methodology discussed by cosmologists are sometimes far from what Popper actually thought and wrote.
I would like to thank Tilman Sauer for suggestions and critical remarks to an earlier version of the paper.