More than countries, it was 'regions' that the Ottoman Empire controlled. Historians comment on this unexpected expansion policy of the Ottoman Sultans that they would only annex a certain part of the country that lay to the boundary of their existing Empire and not engulf them completely. This could be seen as a master administrative move as perhaps the rulers realized that the upkeep of those countries would cost them more.
Therefore to crush them politically was their main motive; they achieved the dual goal of control over the territory but also without bloodshed that would have preceded the capture of countries. They conceptualized the master move of making those regions Vassal and Tributary regions of their Empire! By doing this, they ensured that the ruler of the country was obliged to pay the Empire taxes but run the region of their own. In a way, the Ottoman Sultans saw the move as their 'mercy' on the states!
Though control over the countries varied throughout the medieval ages, the Ottoman Empire was more or less a stable Empire until the rise of nationalism took place in the fag end part of the medieval ages. Important countries that Ottoman Empire captured were (excluding the regions):
These were the major countries that were captured or a part of the Ottoman Empire; other than them even more regions and countries in Asia, Europe and Africa came under the Empire as a part of their Vassal states or Tributary regions. The earliest of these regions was Anatolia from where the Ottoman Movement started and continued to Europe into Serbia. A timeline of the Ottoman Empire would give an idea about how they went ahead with their expansion pursuit.
Tripoli was one of the later captured regions and remained till the very last of the Ottoman Empire. Understandably, Tripoli still has traces and remnants of the mighty Empire that once Ottoman was. The interesting thing to learn about the Empire with the geographical significance is that the region served as a central trade region for the entire world that wanted to trade with Asia through the shortest route possible. The famous Silk Route also once briefly came under the Ottoman Empire but it did not lay claim to the route; instead it also used the route to trade with another golden bird of Asia - India.