Chiral effects, such as the chiral magnetic effect, have gotten interest in a broad range of fields of physics, such as the hadron physics, condensed matter physics, and astrophysics. Since they are originated from the chiral anomaly, which is ubiquitousin the quantum theory of fermions and gauge fields, they can appear regardless of the energy scales, including cosmology In this talk, I will introduce recent studies of the chiral effects in cosmology. One important subject is the baryogenesis from the hypermagnetic helicity decay and the magnetogenesis through the chiral plasma instability. I will also give insights of axion inflation on the baryogenesis. Cosmology with the chiral gravitational effect, which is the counter part of the chiral magnetic effect, will be also discussed.