Who was behind the July 2016 Turkish coup attempt?

On the evening of July 15, 2016, the world was surprised by news of a military coup in process in Turkey. Top politicians, including President Recep Tayyip Erdogan himself, and heads of the military and police were attacked or detained, media outlets were taken over, and armed soldiers took over the streets. After President Erdogan issued a call to action using his mobile phone, Turkish civilians streamed onto the streets and confronted the Turkish military, ultimately thwarting the coup. In the aftermath of the coup attempt, the Turkish government blamed Fethullah Gulen and urged the US government to extradite him, while arresting, suspending or firing hundreds of thousands of Turkish citizens. Gulen for his part condemned the coup and denied any connection to it. Half a year later, the Turkish government was still prosecuting Gulen in absentia, sparring with Germany and Greece about the extradition of Turks allegedly involved in the coup attempt, and warning countries in Africa and Asia about any involvement with the Gulen movement. Turkey has a history of coups, typically being led by the military, with the stated goal of upholding Kemalist values, including secularism, and restoring order. Historically Turkish politics has been dominated by Kemalism, but over the last fifteen years, religious parties have gradually become the most influential actors in Turkish politics, including the Sufi and modernist-leaning movement of Fethullah Gulen, and Erdogan's Justice and Development Party (the AKP). The AKP calls its ideology "conservative democratic," focused on increasing religious freedom in the public sphere and economic liberalism; its critics allege censorship of free press and illiberal authoritarianism.