Like many people, I got through phases in the music I crave. I will listen to KanYe and J Cole for weeks, then I will break out my Led Zeppelin and Steely Dan albums. Right now there is no band hotter for me than the Black Keys.
When I am listening to rock music, I rarely am looking for the hard-hitting, catchy tunes (AC-DC, the Killers); rather I prefer creative, skilled, progressive song writing (Red Hot Chili Peppers, Radiohead). Very rarely will you find music that covers both of these attributes. The Black Keys know how to blend their unique still with melodies that you can't get out of your head all day. (If you haven't read this article about why pop music is addictive, its a must read.)
If your new to the Black Keys, I would suggest starting with their newest album El Camino. It is the easiest album to get into because it is the most "mainstream" of any of their albums. After that, move to their best album Brothers.