Topological superconductivity has attracted great interest in condensed matter physics because of its potential applications in quantum computing. Spin-triplet superconductors are one promising class that can host the topological excitations of interest, but experimental realizations are few and far between. The discovery of superconductivity in UTe2 - a material closely related to known ferromagnetic superconductors such as UGe2, URhGe, and UCoGe - has launched an international effort to investigate its anomalous superconducting phases, which include a spin-triplet multicomponent order parameter at ambient pressure, multiple distinct superconducting phases in the pressure-field space, as well as exotic magnetic field-boosted reentrant phases that live in excess of 60T pulsed fields. However, the normal state of UTe2 also holds amazing complexity, including Kondo/heavy-fermion physics, strong magnetic fluctuations, anomalous low-temperature phases and quantum-critical behavior. I will review our ongoing studies of the anomalous normal state of UTe2 - including studies of the electronic anisotropy and anomalous Hall effects, pressure-temperature-field phase diagrams, magnetoresistance, thermal transport and inelastic neutron scattering experiments - and discuss their relations to the electronic band structure and magnetic correlations.
