In 1979, Egyptian Islamists formed the Egyptian Islamic Jihad (EIJ). The EIJ wanted to overthrow the Egyptian dictatorship and set up an Islamist regime. The EIJ included a faction of Palestinians living in exile. In 1981 the EIJ participated in the assassination of Egyptian dictator Anwar Sadat. Many EIJ members fled the subsequent repression, while the Palestinians were expelled to Gaza. They re-branded themselves as Palestinian Islamic Jihad (PIJ). PIJ aims at the destruction of the state of Israel and the creation of an Islamic state encompassing all of pre-partition Palestine.
By the late 1980s, PIJ had moved into the orbit of Iran through its client in Lebanon, Hezbollah. Both Israel and the Palestinian Authority have opposed PIJ. Between 1987 and 2002, PIJ claimed 17 attacks (mostly bombings and ambushes of public transport buses); from 2002 and 2014, PIJ claimed 14 attacks (mostly bombings of public places).
Mid-stream in the second period of PIJ attacks, another, larger Islamist movement, Hamas, won the Palestinian elections. Hamas evicted the defeated Fatah-led faction from Gaza. Fatah then evicted Hamas from government positions in the West Bank. Since then, Hamas and PIJ have maintained an uneasy relationship, competing for advantage within Gaza while co-operating against Israel.
The co-operative stance of the two parties may be eroding. On the one hand, the on-going Muslim civil war between Shi’ite and Sunni forces people to take sides. Hamas is a Sunni Islamist movement. Iran and Hezbollah are Shi’ite. Since 2014, Iran has greatly increased its financial and arms support to PIJ, leading to a growing role for PIJ in Gaza and the West Bank.
On the other hand, the responsibilities of governing Gaza may be sapping the intransigence of Hamas. The government led until recently by Benjamin Netanyahu slammed tight economic constraints on Gaza in response to Hamas attacks. It repeatedly pounded the living daylights out of Gaza in retaliation for rocket attacks. Those restrictions–generally supported by Egypt, so no one is coming to help the Gazans–have made life in Gaza miserable for the two million people trapped there. Since the fall of Netanyahu, Israel has modified its policy. It has eased restrictions on imports and exports. It has also offered work-permits for 14,000 people. It has dangled the possibility of raising the number of permits to 20,000 under the right security conditions. With a 50 percent unemployment rate in Gaza, Hamas may see some benefit in greater co-operation. As more and more Sunni Arab states normalize relations with Israel, it must be occurring to many Islamists that the “Jewish entity” isn’t going anywhere.
That is one way of understanding the recent outbreak of fighting in Gaza. In April and May 2022, PIJ launched a new round of attacks inside Israel. Israel responded with arrests of PIJ leaders on the West Bank. PIJ countered with rocket attacks directed at Israel. Israel countered with attacks on PIJ members in Gaza. In all this, Hamas did not involve itself in the fighting and Israel did not target any Hamas sites. The West Bank government did not interfere with arrests.
Slowly, radicals may be getting shoved to the margins. Or perhaps not.
 See: Isabel Kershner, “After Three-Day Conflict In Gaza, Cease-Fire Holds,” NYT, 9 August 2022.
 Not necessarily by a lot. The recent fighting led to a cut-off of imports for a week. By the end of that time, Gaza was almost out of fuel for its electric generators.
 The limits on Arab workers in Israel sprang from the Arab terrorism, especially suicide bombings, of past times.