Dumbbells are great to have in the home because you can perform so many types of exercises with them. When I lift weights, I always work out the most common muscles such as my arms and legs. I hardly focus on my upper back. Craig Ballantyne has a great video which demonstrates upper back exercises using dumbbells which you can do at home.
Note: Always get clearance from your health care provider before performing any new exercise regimen. Seeking guidance from a fitness professional is also encouraged.
You can learn more about Craig Ballantyne and his exercise programs by visiting Turbulence Training.