Relatives of captives have reacted with fury and demanded PM Benjamin Netanyahu step down over the crisis.
In Israel, the plight of the captives dominates the political and news agenda, with major rallies calling for their release.
Some have been freed in return for Palestinian prisoners, but 138 remain trapped in Gaza.
Prime Minister Benjamin Netanyahu says bringing them home safely is a priority. But he says so while his military bombs Gaza without mercy.
Relatives have reacted with fury at a meeting with the prime minister and his war cabinet.
Some are even demanding Netanyahu step down.
What do people in Israel think?
Presenter: Neave Barker
Udi Goren – Cousin of one of the captives detained in Gaza, who has taken part in the “Bring Them Home Now” campaigns
Gershon Baskin – Former hostage negotiator and founder of the Israel-Palestine Center for Research and Information, a joint public policy think tank
Akiva Eldar – Political analyst and author of, Lords of the Land: The War Over Israel’s Settlements in the Occupied Territories, 1967-2007