Osman was succeeded by capable men. His son, Orhan Ghazi (fl.1324 - 1362), was a competent leader of the clan and continued his father's goal of expansion. The conquest of the important Byzantine fortified city of Bursa in Anatolia was completed by Orhan—Osman was suffering from gout by this time, and left battle to others; he died shortly after—who made Bursa the new Ottoman capital.
The defeat of Constantinople and the Byzantine Empire was an important step to increasing the Ottoman territory and power. A period known as the Byzantine-Ottoman Wars began in 1299 and culminated in the taking of Constantinople in 1453, a year and event that I have written about before.
Orhan captured several areas, including Gallipoli in 13543 (at the time called Kallipolis), getting closer to the European mainland. A three-year siege brought Nicaea under Orhan's control in 1331, and Nicomedia in 1337.
Then Orhan made a bold move: he turned his attention to Karesi (now Balıkesir, in the Marmara region of Turkey). Its ruler had died and the deceased's two sons were fighting over the succession. Orhan claimed he was coming in as a bringer of peace. This sounded good, but Karesi was Muslim, and attacking fellow Muslims was not acceptable.
There was, however, no one strong enough to oppose him. One brother was killed in the fighting, the other was captured, and Orhan took over a large Turkish area. This was the start of expansion to the East.
Fighting between brothers over succession was quite common in the Turkish world (and elsewhere, to be fair). In fact, Orhan had a brother whom some scholars think might even have been older. Rather than being a rival, however, he provided valuable help to Orhan. Tomorrow I want to tell you about Alaeddin Erden Ali Pasha, who (we are told) probably contributed as much to the success of the growing Ottoman Empire as Orhan's military choices.