Quantum phase slips (QPS) are the primary excitations in one-dimensional superfluids and superconductors at low temperatures. They have been well characterized in most condensed-matter systems, and signatures of their existence have been recently observed in superfluids based on quantum gases too. In this review, we briefly summarize the main results obtained on the investigation of phase slips from superconductors to quantum gases. In particular, we focus our attention on recent experimental results of the dissipation in one-dimensional Bose superfluids flowing along a shallow periodic potential, which show signatures of QPS. This article is part of the themed issue ‘Breakdown of ergodicity in quantum systems: from solids to synthetic matter’.