Neutrino nonstandard interactions (NSI) alter the behavior of neutrinos beyond the predictions of the Standard Model, leading to significant implications for the expansion history of the Universe, loss of neutrino free streaming, among others. These modifications leave observable imprints on cosmological data sets such as Big Bang Nucleosynthesis (BBN), the Cosmic Microwave Background (CMB), Baryon Acoustic Oscillations (BAO), and the large-scale structure (LSS) of the universe. In this talk, we will review the state-of-the-art cosmological constraints on the neutrino NSI parameter space, with a particular focus on the paradigm of neutrino self-interactions. We will discuss current anomalies and the most stringent bounds, highlighting how cosmological observations serve as powerful indirect probes complementary to terrestrial neutrino experiments.