I have always been interested in this type of photography. I wish people would describe their gear, approach, and challenges with it.
Bear in mind, I've only been attempting DSO (deep space object) photography for a few months, so my thoughts and input are worth what you paid
Here are the cliff notes on challenges in my experience so far:
1. Conditions need to be near perfect, any wind or clouds can ruin a night planned in advance. The best time for astrophotography is within a few days of a new moon, so figure in the small number of days that entails and eliminate the ones with bad weather or when you just can't do it, and the number of prime opportunities per year decreases quickly. That's not to say you can't shoot with the moon in the sky, it just becomes more challenging and typically requires more expensive equipment (see #4). Also, if you live a larger city light pollution that makes things more challenging as well. It can be done....at more expense and challenge. I'm lucky enough to live a relatively darker area compared to a large city.
2. Time investment: So when you do luck upon a good night with the right conditions....don't plan on sleeping much. The setup alone i.m.e so far takes around an hour. And that's before zoning in on a target. It can be done quicker when things go just right....unless you get into the big really expensive gear which is another animal I can't address. One night I started setting up at 9:30 and didn't start imaging until 1 am. Mostly due to rookie mistakes but I can assure you I'm not alone. Then, once you're set up, find your target, focus, etc the actually imaging starts. That can be anywhere from a couple hours to to multiple nights, but again don't plan on sleeping much the nights you plan on shooting.
3. Processing: Once you finally get some data worth working with, the post processing is also time consuming. The more experience you have with photoshop the shorter the learning curve will be, but it's not intuitive. Like anything else photography related there are plenty of resources online to help though.
4. Expense: Again as with anything else photography related, this is always a loaded question. You can make it as cheap or as expensive as you want, with somewhat correlated results given a large number of variables. With that said, it isn't cheap. At very minimum you'll need a DSLR and decent telephoto or longer focal length prime lens, and a star tracker/guiding mount. From there the wish-list grows...higher end GEM style mounts, telescopes, guiding scopes, filters, PC programs, power sources for remote shooting, etc, etc.
I'm happy to answer any questions you have given my ability and lack of experience. If you haven't already check out the Cloudy Nights forum, it's a great resource to get a feel for what all is involved and learn if you decide to take the plunge.