Reliability took a hit from using several lower quality parts, after 2000 models, but Volvo has still got several components that are very durable. Don't mistake this by thinking it's a long lasting trouble free car, because it's not, and when it comes time for repairs, you'll be shocked at the bill. But most car makers went with lower quality parts after 2000.
As of now, after been sold to a Chinese company, Volvo has quite some trouble with the electricals, and on some models with the transmission, even at low miles.
Quality did arguably go down after around 2000, but that is probably more due to the fact that the technology went up as Volvos were brought into the 21st century. I'm a big fan of the older Volvos, but also the newer ones alike. Transmission issues aren't a problem after about 2007, especially in the XC90 when Volvo stopped using the GM made gearboxes, which were a very big mistake. No problems on the latest generation of Volvos (post 2007) - these cars often rack up well over 100k miles in the first couple of years without serious issues, and no more issues than the equivalent BMWs, Mercs, Audis, etc.
None of the cars made these days are as dependable as their older versions, if looked after. Not even Japanese cars - just read the reviews of later-model ones, especially from North America. Cars are just too complicated with necessary computers to comply with emissions and safety regulations, which as you know if you have a desktop, are not always dependable. Just the way things are, unfortunately. The bodywork doesn't rust these days - good rustproofing or zinc coating, the engine blocks and valves don't usually give problems. It's what's attached to them all that causes expensive grief.