
Location of Transnistria. In red the territory controlled by the Transnistrian authorities, with disputed territories alternatively coloured. The Republic of Moldova considers Transnistria as an autonomous region within its own jurisdiction.
The area of Transnistria has a diverse history of Roman, Slavic and Turkic presence. In the Middle Ages it became part of the Grand Duchy of Lithuania and subsequently the Polish-Lithuanian Commonwealth, although it was ruled by local Moldavian princes. In the 17th century the Principality of Moldavia became a vassal of the Ottoman Empire. In 1792 and 1793 the Russian Empire annexed Transnistria from the Ottoman Empire, and Moldova followed in 1812. The remainig Romanian principalities were united in 1859 and formed an independent kingdom in 1878 with Russian support, but Moldova stayed within the Russian Empire even though the Moldavian language is very similar to Romanian, and by some even considered as equal.
After WW1 Romania was awarded a lot of territory, mostly from the Kingdom of Hungary but also Moldova and Bessarabia from the Russian Empire up to the Dniestr river. In response, the newborn Soviet Union established the Moldavian ASSR in 1924 on the other side of the river as part of the Ukrainian SSR.

Situation between the two world wars.
In 1940, Moldova was annexed by the USSR as part of the Molotov-Ribbentrop Pact and joined with the existing ASSR to form the Moldavian SSR. In 1941 Romania joined Nazi Germany in the invasion of the USSR and resumed control over Moldova but also annexed vast territories at the other side of the Dniestr as far as even Odessa. This annexed territory had only a 10% minority of Moldavians, and many other ethnicities in the region were brutally oppressed during the occupation, leading to the deaths of up 250,000 people. These events still feed anti-Moldavian feelings today in Transnistria.

Romania from 1941-1944. The Axis Powers granted the Transnistria area (incuding vast parts of present-day Ukraine) to Romania as a compensation for losing Transylvania to Hungary. The added territories in the northeast had only 10% Moldavians/Romanians and oppression of other ethnicities was severe.
In 1944 the Red Army forced the Romanians back and reestablished the borders of 1940 and the Moldavian SSR, with territories on both sides of the Dniestr, even though the percentage of Moldovans was far lower in Transnistria than west of the river.
In the 1980's nationalist movements gained popularity in Moldova, and things started to polarise quickly after the declaration of independence in 1990. The rights of non-Moldavian ethnicities was severely limited by the nationalist policies pursued by the Popular Moldavian Front, which led to resistance by the large Russian and Ukrainian minorities in Transnistria, ultimately resulting in the 1992 War of Transnistria. The Russian military intervened to end the conflict which resulted in the current situation of what is frequently referred to as a 'frozen conflict'.
Several attempts have been made to solve the conflict involving both Russia and Western countries but without result so far. Periods of thaw are followed by provocations from both sides. The Transnistrian authorities are accused of limiting individual freedom (especially with respect to Moldavians who form 30% of the population) and involvement in illegal activities, but at the same time the Moldavian government is accused of border provocations and in general held accountable for creating the hostilities towards non-Moldovans in the early 1990's. The recent actions by the Ukrainian government concerning the Ukrainian-Transnistrian border are further escalating the situation.
Currency
Transnistria uses its own currency which is the Ruble, consisting of 100 Kopeks. The current version is actually the Third Ruble after redenominations in 1994 (1000:1) and 2000 (million to one). In 2000 the first coins were minted by the Polish Mint which led to protests by the Moldavian government. In 2004 the Polish Mint cancelled the contract, and Transnistria opened its own mint in its capital Tiraspol a year later. In 2015 the Transnistrian Republican Bank introduced a novelty by issuing coins made of composite material rather than metal, to replace the banknotes of 1, 3, 5 and 10 Rubles.
The Transnistrian Ruble is freely convertible but only in Transnistria itself. It traded around 11 Rubles per USD in 2014 but it's hard to find recent data.
https://en.numista.com/catalogue/transnistrie-1.html