1. Arming the YPG
From the 2003 US invasion of Iraq to Washington's latest decision to arm the YPG in Syria, relations between Turkey and the US – NATO allies and partners in the war against Daesh – have been repeatedly tested.
Last week US President Donald Trump authorised the Pentagon to equip "Kurdish elements" of the US-backed Syrian Democratic Forces (SDF), which the YPG dominates, in a bid "to ensure a clear victory" over Daesh in Raqqa, Syria.
Ankara condemned the decision. Turkey pointed to the links the YPG has to the PKK, which both sides agree is a terrorist group. The US says it needs the YPG in its battle against Daesh in Syria, a claim Ankara disputes.
Ongoing US support for the YPG is likely to be a key issue for the Erdogan-Trump meeting during the Turkish president's May 16-17 visit to the United States.
Turkey recently ended its "Euphrates Shield" military operation inside Syria aimed at driving Daesh, the PKK and other terror and armed groups away from its border with Syria. Turkey believes that arming the PKK-linked YPG is a setback for its goal of securing its border with Syria and making northern Syria safer for people enduring a devastating war that is now in its seventh year.
Erdogan appeared to offer Trump a way out of the impasse, suggesting the US decision was a relic of policy from the Obama era, counter to the two countries' strategic interests, and the result of the new presidency still being in a "transition period."
Ankara wants the US to cooperate instead with the Turkey-backed FSA (Free Syrian Army) to battle Daesh in Syria.
Turkey pointed out that Raqqa is a predominantly Arab city and its residents may not take kindly to being controlled by the predominantly Kurdish YPG.
Raqqa is also an oil-rich province, which could potentially become a source of income for the YPG, and subsequently the PKK, if the YPG does not cede control to the local population once Daesh is driven out of the city.
According to the US think-tank The Washington Institute, "Trump could convince Erdogan to make a deal on Raqqa by agreeing to support a potential Turkish campaign against Sinjar, an emerging PKK base that straddles the Iraq-Syria border."
2. Extradition of Fethullah Gulen
Another unresolved issue from the Obama-era is Ankara's demand for the extradition of Fethullah Gulen. The Turkish president is likely to push for Gulen's extradition to face charges of masterminding the July 15, 2016 failed coup in Turkey. Ankara blames the Gulen network or "FETO" (Fethullah Terrorist Organisation) for the failed attempt to overthrow the president and government, which left 249 people dead and over 2,000 wounded, when disaffected elements in the military and police attempted to take control of the country.
The administration of former president Barack Obama did not act on the long-standing extradition request, even after the failed coup. Erdogan will be looking for Trump to reverse that. Gulen, who denies any involvement in the failed coup, has been living in self-imposed exile in the US state of Pennsylvania since 1999.
However, regardless of what Trump might say on the issue, whether Gulen can be extradited depends not on the presidency, but on the US judicial system.
3. Bilateral trade & investment
Not only politics, but business also ties the United States to Turkey. Two luxury towers in the county's biggest city and commercial hub Istanbul bear the "Trump" name under a licencing deal.
"I have a little conflict of interest 'cause I have a major, major building in Istanbul," Trump said last year. "It's a tremendously successful job. It's called Trump Towers – two towers, instead of one, not the usual one, it's two."
Despite differences on the issues of Syria and FETO, business ties between the two countries are strong and growing.
Some 1,600 US companies do business in Turkey, employing over 60,000 people. And the US uses Turkey as a regional export base for more than 80 countries.
But there is much room for growth. Despite Turkey's economy being valued at $960 billion, business advocacy organisation the US-Turkey Business Council says bilateral trade is worth only $20 billion, with a mere 3.9 percent of Turkish exports destined for the US market and 5 percent of its imports originating from the US.
Boosting the commercial relationship is expected to be on the agenda in the Turkey-US talks.
4. Turkish banker's trial in US
One wrinkle in the hope for expanded business ties is the arrest of Halkbank Deputy General Manager Mehmet Hakan Atilla in March on charges of aiding Iran to circumvent US rules on trade with Washington's regional nemesis.
The US has accused Atilla of using his position at the bank to help Turkish-Iranian gold trader Reza Zarrab, who is also being held by US authorities, of conducting hundreds of millions of dollars of illegal transactions through US banks on behalf of Iran's government and other entities in that country.
US prosecutors say such actions contravene sanctions against Iran. The bank has denied any wrongdoing.
Ankara says Atilla's arrest was a "political" move and that former US attorney Preet Bharara – who led the investigation against Atilla and Zarrab and was fired in March by Trump – has links to FETO.