Maps are taken from https://www.oldmapsonline.org
The Principality of Moldavia was the westernmost part of the Mongol Empire from 1241 to 1346. Events before then are not important for understanding how Moldova became an independent republic from Romania. Before then the region was occupied by Turkic peoples.
After independence, the Principality of Moldavia was formed in 1346, ruling the land between the Danube Delta, the Carpathian mountains, and the Dniester River. In 1812 the Treaty of Bucharest was signed, granting what is now the Republic of Moldova to the Russian Empire. This was the first time Russia controlled any part of the historic Principality of Moldavia.
The Principality of Moldavia merged with Wallachia in 1859, renaming themselves as Romania in 1862.
Moldova was briefly reunited with the Kingdom of Romania after World War I, and during the Second World War, the Soviet Union retook Moldova in 1940.
In 1991 Moldova declared independence during the ongoing Transnistria War. Ukrainians formed a plurality of the population of Transnistria during the Soviet Union. When the Soviet Union dissolved Transnistria had a Romanian/Moldovan plurality. The Transnistria war saw Moldova fighting against Russian-backed rebels, leading to a stalemate. After the war, Transnistria has remained a pluralistic society split evenly between Russians, Moldovans, and Ukrainians.
Transnistria today has major restrictions on freedom of the press, and violations of civil liberties are reported by groups like Freedom House. Polling data is sparse on all issues. The last presidential election has no polling data available on its Wikipedia page. The latest parliamentary election was uncontested in a majority of districts. Even Russian papers declared Transnistrian elections as undemocratic. It is ranked as not free by Freedom in the World.
That is the status of Transnistria.
References:
https://en.wikipedia.org/wiki/History_of_Transnistria