If you have a tricky lower back, barbell rows can be troublesome, especially when using bodybuilding techniques like drop sets. Also, many lifters don't feel barbell rows in their upper backs much. The solution? Inverted rows.
Inverted rows are a staple exercise in my program and have become my favorite rowing variation. The key to making them a viable strength and muscle builder as opposed to a foo-foo exercise is that you have to treat them as a strength and muscle builder. That just means that rather than going through the motions, you have to push yourself and get progressively stronger over time.
The most basic form of progression is obviously adding weight, either by stacking plates or wearing a weighted vest. Vests make it a little easier if you have them, but both options are great. In fact, using the plates increases the core demands, which is a nice bonus.
After going heavier, I also like to end with a higher-rep burnout set, which is something I wouldn't recommend with free-weight rows due to safety concerns for the lower back. When using plates, I'll often end with a drop set, which will leave your upper back and forearms burning like crazy.