Desmond Miles is the modern-day protagonist who descends from Altaïr and Ezio in the early Assassin's Creed games.
Desmond is abducted by Abstergo and forced to use the Animus, where he relives the memories of his ancestors. His lineage includes Altaïr Ibn-La'Ahad and Ezio Auditore, allowing the modern-day storyline to connect the historical campaigns of the first games. Desmond later escapes and joins the Assassin cause.
His modern-day sections appear prominently in Assassin's Creed, Assassin's Creed II, Brotherhood, Revelations, and Assassin's Creed III. They frame the historical adventures as part of an ongoing conflict between the Assassins and Templars in the present day. Desmond's experiences also involve the Bleeding Effect, through which Animus exposure affects his skills and perceptions.
Clay Kaczmarek is another modern-day Assassin connected to the Animus, while William Miles is Desmond's father. Layla Hassan becomes the main modern-day character in later games, beginning with Origins. Those characters are related to the modern storyline but are not the answer here.