Not yet reviewed by Pith; the record is open.

We present a detailed study of the cosmic star formation history over $90$ per cent of cosmic time ($0\lesssim z\lesssim4$), using deep, radio continuum observations that probe star formation activity independent of dust. The Low Frequency Array Two Metre Sky Survey has imaged three well-studied extragalactic fields, Elais-N1, Bo\"otes and the Lockman Hole, reaching $\sim20\,\mu\rm{Jy/beam}$ rms sensitivity at $150\,\rm{MHz}$. The availability of high-quality ancillary data from ultraviolet to far-infrared wavelengths has enabled accurate photometric redshifts and the robust separation of radio-bright AGN from their star-forming counterparts. We capitalise on this unique combination of deep, wide fields and robustly-selected star-forming galaxies to construct radio luminosity functions and derive the cosmic star formation rate density. We carefully constrain and correct for scatter in the $L_{150\,\rm{MHz}}-\rm{SFR}$ relation, which we find to be $\sim0.3\,\rm{dex}$. Our derived star formation rate density lies between previous measurements at all redshifts studied. We derive higher star formation rate densities between $z\sim0$ and $z\sim3$ than are typically inferred from short wavelength emission; at earlier times, this discrepancy is reduced. Our measurements are generally in good agreement with far-infrared and radio-based studies, with small offsets resulting from differing star formation rate calibrations.