I have a friend who visited it and came back with one of the funniest post-Cold War stories I know. It's representative enough of this stuff that I'm going to recount it, even though most of its value resides simply in being funny.
So my friend is a very nice and friendly guy, who travels all over the world. He speaks Romanian well, but not too much Russian. The border checkpoint, naturally, was manned only by a few friendly folks who spoke nothing but Russian.
He shows them his papers, and they manage to understand each other only to the extent that he explains he wants to visit Tiraspol, and that he's a tourist. All of this mostly in sign language.
So this guy apologizes, tells my friend to wait, and goes off through a door in the back. Almost an hour later, he returns with someone who speaks a little Romanian. My friends explains the whole I wanna visit Tiraspol, I'm a tourist thing all over again. More discussion and paper checking ensues.
Another hour later, the two guys leave again, and return with a third soldier. This time, someone who speaks excellent Romanian. The whole explanation gets repeated. They finally give him the visa, wish him good luck and safe journey -- and one of guys pats him on his shoulder and apologizes.
Sorry, man, he says, you look like a nice guy and I'm sure you really are a tourist. But you have to understand, when someone shows up at the border and claims they're a tourist, we usually find out he's definitely not a tourist.
Edit: every other event of his trip was equally funny, except it involved no public authorities :). From what I've heard, Tiraspol isn't too bad a city -- but do remember this is basically still a Soviet state. I'm sure it's very bad if you piss of the wrong person.
Yeah, that was my experience going in too - took about six hours at the border to get two cars through - and if it hadn’t been for my wife who speaks fluent Russian, it would’ve been no dice.
Tiraspol feels like many post-soviet cities, and reminded me of Volgograd - the only real difference is the ubiquitous and contemporary soviet imagery.
Oh, we did - had a box full of pot noodles, and various Union Jack branded tat - you’d be amazed at how far a touristy biro and tiny tin of biscuits will get you.
On the other hand, it sucks when you’ve spent six hours buttering up an entire border station, and then the shift changes, as happened when trying to get into Uzbekistan just after a bombing in Tashkent. Ended up having to sleep in a brothel in a Kazakh border town, as the border was truly closed, and after 30 hours of wakefulness we were ready to drop - and the nearest hotel was in Shymkent.
Yeah, it's an odd old place - it really is still a Soviet state - with secret police to match. We had a shadow in Tiraspol, shook them because we could, as taking them on a wild goose chase is almost sport, and... then found it rather hard to get out of the country, as a result - a sizeable bribe had to change hands.
Still, it's worth visiting, for a day or two, once.
There's a lot more to Transnistria. Russia wants it as a strategic point of access to Europe. There are roads purposely build for quick access with tanks (big, heavy, concrete roads, reinforced with rebar - your car usually makes a clunking sound as if you're on a train). So they support the region with preferential natural gas prices (sometimes the bill gets completely tagged to Republic of Moldova). At the time when URSS collapsed, and the split happened - most of the heavy industry was on the Transnistrean side (including weapons factories), so it was big loss for Republic of Moldova. The Army 14 of the URSS never left Transnistria, and Russia still refused to call them back. [ https://ro.wikipedia.org/wiki/Implicarea_Armatei_a_14-a_%C3%... ]
It's a semi-lawless land, used sometimes as a hiding spot for criminals, assassins, etc. Gun trafficking is at home there. When on bike, I managed once to pass the border without being checked (and I didn't notice I didn't have my papers with me, I almost got stuck in there) - you're basically at the whims of the border patrols.
There are a few villages that belong administratively to Republic of Moldova (I visited Coșnița [coshnitza] with a friend, that is one such village) - this state of affair came with great cost of lives, and people there still remember the price they paid. Tensions sometimes get high - in 2012 a drunk guy was shot and killed by the border patrol, as he was traversing the bridge - people were literally picking up forks and scythes to avenge him [ http://www.ziare.com/europa/moldova/moldovean-impuscat-de-ru...]
Transnistria: A land in limbo: CNN: 3m 22s: https://www.youtube.com/watch?v=mAReDKkT9TA
Transnistrian Independence Day 2017: A travel blogger who doesn't over-do it with commentary: 3m 9s: https://www.youtube.com/watch?v=q28ZONQIHK0
It has its own "borders, police, military and currency"!: Another travel blogger, well narrated and short: 8m 15s: https://www.youtube.com/watch?v=-m-9Q5CkEvE