I briefly touched on Pombaline architecture in my post Who are they? Famous names on the streets of Portugal. Here I mention the style is named after a chap by the name of Sebastião José de Carvalho e Melo, who became known as the Marquês de Pombal.
 
The Marquês de Pombal is credited for his leadership role during the rebuilding of Lisbon following the 1755 earthquake (and ensuing fire and tsunami). At the time he was the Secretary of State for Foreign Affairs, but quickly took the leading reigns after the king at the time José I, essentially curled up in a ball and prayed for it all to be over (or so the story goes). Pombal subsequently became the prime minister of Portugal.

Portugal's Manueline architectural style is named after its key influencer, King Manuel I, who served as Portugal’s head honcho from 1495-1521. This wasn’t a bad time to hold the reigns, as it was during this period that Portugal held the power of the pepper.
 
As you might remember from my post A brief history of Portugal, the Portuguese were incredibly influential during the Age of Discovery. Portugal’s brave seafaring souls proved it was possible to sail across the world without dropping off the end, and in a fortuitous twist, discovered you could become rather wealthy if you collected and traded spices from lands you stumbled upon along the way.