1- Ban on Turkish ministers
Relations took a bad turn in recent weeks after several Turkish ministers were refused permission to address public rallies in Germany.
Around 1.4 million eligible Turkish voters live in Germany and their support could play an important role in presidential referendum next month.
German Chancellor Angela Merkel's government said local authorities took the decision to stop Turkish ministers from campaigning, not her government.
But she supported the "decisions that were taken".
Omer Celik, Turkey's minister of EU Affairs, said the rallies couldn't have been cancelled without the German government's consent.
"There is a systematic prevention [being implemented against Turkey]."
The four rallies were planned in German towns of Gaggenau and Frechen and city of Cologne. But the authorities refuse to give permission citing security concerns.
Turkey's Finance Minister Nihat Zeybekci and the Foreign Minister Mevlut Cavusoglu subsequently moved their public meetings to a hotel and the consulate where only a small number of people could come.
2- The Nazis and spies
Turkey said Germany's refusal to allow its officials to campaign was a ban and infringed on their rights. Erdogan likened it with its "Nazi-era practices."
The reference to the World War II regime, responsible for killing millions of people, was met with condemnation in Germany.
Merkel said she didn't take the statement "seriously".
Just days after the spat, the German domestic intelligence agency accused Turkey of spying on its citizens living in Germany.
3- Old wounds
In Turkey, the diplomatic tussle has brought back the memories of the failed military coup last July when Ankara said the European Union (EU) didn't reach out to help.
"Delaying tactics on Turkey's EU membership process and the disappointing attitude after the failed July 15 military coup attempt had already pushed trust toward Germany to a historical low," Daily Sabah said in an editorial on Thursday.
Uncertainty surrounding the proposed inclusion of Turkey in the European bloc has been a thorny issue between Ankara and Berlin for months now.
4- Dual policy
Turkey often accuses Germany of backing the PKK that carries out deadly attacks in Turkey.
Groups allied with the PKK, which has been declared a terrorist organisation by Turkey, EU and the US, often organise rallies in German cities.
On the other hand, Berlin regularly criticises Turkey for suspending thousands of people suspected of being aligned with the coup plotters.
5- Arrest of German journalist
The arrest of Deniz Yucel, a reporter for Germany's Die Welt newspaper, in Turkey on terrorism-related charges in February has further strained ties.
Erdogan called Yucel, a "German agent and member of the PKK".
Germany is demanding his immediate release.
6- The refugee question
Turkey has helped stop the flow of refugees into the EU where the migrant crisis has become a serious political issue.
Germany played an important role in reaching that agreement.
Turkey says European politicians have continuously tried to derail negotiations on the visa-free travel process.
Erdogan has said previously that Turkey might pull out of the deal, opening the floodgates for an influx of refugees into Europe.
But despite the mounting tension, the agreement still holds and both sides are trying to find common ground.
The two countries are strong trading partners. Germany remains the single biggest export market for Turkish goods.
Austria and Netherlands have also jumped into the fray.
Austrian Interior Minister Wolfgang Sobotka said he was introducing a law that would stop foreign politicians from campaigning on its soil. That law also applies to Turkey, he said.