In this review, we present a summary of our experimental results suggesting that the superconducting ferromagnet UCoGe is a spin-triplet superconductor, along with some of the basic physical properties of UCoGe in the normal state. We show experimental evidence that superconductivity in UCoGe is mediated by longitudinal ferromagnetic fluctuations predominant above the superconducting-transition temperature T-SC. This is obtained from the tuning of ferromagnetic fluctuations and superconductivity by changing the external field along the magnetic easy axis, the c-axis. In addition, we show that the spin susceptibility perpendicular to the spontaneous magnetic moment, which is probed by Knight-shift measurement, is almost constant in the superconducting state. The behavior of the susceptibility and the invariance of the spontaneous moment below T-SC can be consistently explained by the equal-spin pairing state with a large exchange field along the c-axis.