At present there are no foreign embassies located in Jerusalem. Though Israel considers the city in its entirety—East and West—as its capital, all foreign governments with embassies in Israel maintain them in Tel Aviv. There are, however, foreign consulates located in both sides of Jerusalem.
For instance, Italy's consulate keeps offices in East and West Jerusalem: in the East to work with the Palestinians and, in the West, to assist "the Italian Jewish community of Jerusalem." The description on their website doesn't mention Israel.
An embassy is the diplomatic headquarters located in a host country, generally headed by an ambassador. It is standard practice that a government's embassy be established in the host country's capital, and that there be only one embassy and one ambassador designated per host country.
Consulates, on the other hand, generally do not operate in the context of the diplomacy between two countries. They do tend to work in coordination with the embassy and its mission, and can perform many of the same services. Yet, consulates are smaller is status and usually function in a bureaucratic capacity, handling visas, passports, trade, education, and so on.
For example, the United States has diplomatic relations with Germany. Accordingly, the US embassy and its ambassador are located in Berlin. However, Washington also has consulates located throughout the country: in Dusseldorf, Frankfurt, Munich, and elsewhere.
The matter of embassies and consulates is normally not a contentious one. With Jerusalem, the issue is a bit more involved.
The present international status of Jerusalem dates back to 1948 and 1967. After the 1948 war between Israel and the Palestinians (and the surrounding Arab states), Jerusalem was divided into West and East: the former became the capital of Israel and the latter went to Jordan. (As part of the armistice, the West Bank was assigned to Jordanian control and Gaza to Egyptian control; hence twenty years of delayed sovereignty for what was supposed to become the state of Palestine.)
During the June 1967 war, or Six-Day War, in addition to Egyptian and Syrian territory, Israel occupied the Palestinian territories of the West Bank and Gaza, along with East Jerusalem. Israel would then annex East Jerusalem, meaning Israel now considered it Israeli.
Conquest and annexation of territory contravenes international law, specifically the UN charter (Article 2) and the Fourth Geneva Convention (Article 47), both to which Israel is a signatory. Moreover, following the Six-Day War, the UN Security Council passed Resolution 242, which emphasizes "the inadmissibility of the acquisition of territory by war." Security Council resolutions have the force of law and are actionable.
Since 1967, Israel has encouraged and facilitated the transfer of its citizens to live in occupied East Jerusalem. This transfer is also in contravention of international law, particularly the Fourth Geneva Convention (Article 49). Today, roughly 200,000 Israeli settlers live in East Jerusalem.
Especially in light of UN 242's call to "achieve a peaceful and accepted settlement," the illegal post-1967 situation has required—and has yet to receive—diplomatic resolution. This illegal postwar situation, which we call the Palestine-Israel conflict, has existed now for fifty years, largely due to Israeli intransigence and US consent.
Any diplomatic settlement of the conflict will have to address a core list of issues. Those issues are: borders, territory, settlements, East Jerusalem, and refugees. East Jerusalem is therefore central to the diplomatic agenda. It is also fundamental both to Palestinian hopes of statehood and a lasting peace between Israel and Palestine.
For fifty years, the United States has played a direct role in preventing a solution to the conflict (see chapter 5 of my Straight Power Concepts in the Middle East for a summary). Nevertheless, in small increments, moments of progress took place during the peace process (1991-2001). And on paper, the United States upholds the two-state solution, namely, two independent states—Israel and Palestine—based on the post-1948 borders, called the Green Line. The issue is simply one of willingness. Resolution of the conflict is very much attainable.
Trump’s decision to move the embassy from Tel Aviv to Jerusalem will dramatically increase the difficulty in getting any diplomacy underway. There is supposedly a peace plan in the works, led by Trump's son-in-law, Jared Kushner, but nothing of any kind of substance, beyond a few recently made blank utterances, has been produced.
The decision will also further legitimize Israel's illegal expansion in the West Bank, potentially inspire further brutality toward Gaza, as well as encourage rightwing elements within Israel's government. (Encouragement of rightwing elements has, after all, been a leitmotif for this president.)
Given the importance of East Jerusalem to the Palestinian cause, the city's overall importance to the Arab world, and its religious significance to billions of people, Trump has risked much for many in an effort to satisfy a few.
Upon word that the president was for sure going to make the announcement, the US consulate in Jerusalem alerted its staff, while the State Department warned embassies around the world. The immediate reaction was concern for security.
In general, the response to a good idea is not to batten down the hatches.