Since their formative years the band has gone through many lineup changes, most significantly after the death of their leader Ēriks Ķiģelis in 1985. Since then Ainars Virga has been on the forefront of Līvi creative output. To this day they have released eight studio albums and two live recordings.
Līvi officially disbanded in 2010 following the death of Jānis Grodums.
In 2013, the band reformed for the in memoriam concert of Grodums.