In 2000, Hafiz al Assad died, Parliament changed the required presidential age from 40 to 34 so al-Assad’s son could run. Bashar al-Assad ran unopposed, winning with 92% of the vote. Israel bombed Damascus in 2003 in response to Syria’s ties and military support to Hamas and Hezbollah. Information obtained from Wikileaks showed that military transactions between Syria and Hezbollah have continued.
In 2005, Syria was linked to the assassination of then Lebanese leader Rafik Hariri; possibly in support of Hezbollah. A UN tribunal will be held in Lebanon and the worry is that this will spark a conflict since the indictment will involve Hezbollah some ranking Syrian officials.
This is all part the perpetual antagonism between the West (including Israel) and Iran, Lebanon, Syria, and depending on the leadership, other areas of the Middle East.
The two main international issues that Syria is facing have to do with Israel and Lebanon, two of its neighbors.
With Israel, the major issue has to do with the Golan Heights. Syria wants Israel to return this area to it. Israel took the Heights in the Six Day War in 1967 and does not want to return it.
Perhaps Syria's biggest international issue has to do with its involvement in the politics of Lebanon. Syria occupied Lebanon from 1976 to 2005 and still continues to have a great influence on its politics. There are allegations that Syria was behind the assassination of the Lebanese leader Rafik Hariri in 2005. The United States alleges that Syria continues to arm Hizbullah, which is an Islamist organization that controls much of Lebanon and is in tension with the official government of the country.