What was the succession of ownership of the land now known as Israel, Gaza, and the West Bank prior to May 1, 1949?

After WWI, as another answer notes, the British took control under a League of Nations Mandate (which was kept under the UN as well). The Ottoman Empire owned it prior. In 1949, following the end of the 1948 Arab-Israeli war, Israel was established in the territories that do not include the Golan Heights, West Bank, and Gaza. It also did not have control over East Jerusalem, only West Jerusalem. Syria held the Golan Heights, Egypt occupied Gaza, and Jordan occupied the West Bank. Any annexations (such as Jordan's attempt to annex the West Bank) were considered unlawful and rejected by most of the world's nations.

Following the 1967 Six Day War, Israel seized the Golan Heights, the West Bank, Gaza, and East Jerusalem. It also seized the Sinai Peninsula, up to the Suez Canal. It almost immediately annexed East Jerusalem, but did not formally declare that it was doing so. Still, most people recognize it as an annexation. The other areas were never annexed in the same way, though settlements almost immediately began to spring up in the newly occupied territories. The Sinai was returned to Egypt following a few interim agreements in the 1970s and the Israeli-Egyptian peace treaty in 1979 that returned the entire Sinai in return for peace (other things were included in the treaty, but that's another story). Now Israel was occupying the West Bank, Gaza, and had informally annexed East Jerusalem. Israel remained occupier of the Golan Heights.

I can't talk about the situation today, but a cursory google search will tell you which ones Israel is still in control of. That's pretty much the narrative of the land ownership exchanges going back almost 100 years. If you'd like more information, feel free to ask!