With a compact refrigerator, it is all about space. A compact refrigerator has to work well, but take up the minimum amount of space and offer the maximum usable capacity.
This involves trade offs: no freezer, small door bins and problems putting in larger items such as drink bottles. These fridges offer manufacturer stated capacities of less than 5 cubic feet, and the actual usable space is considerably less. Models like the Frigidare BFPH31M6LM are only about 20 inches deep, but they only offer 0.9 cubic feet of freezer space and 2.2 cubic feet of refrigerator space: not enough to hold much food.
Compact refrigerators may also be somewhat inefficient: although they offer much less space than their larger cousins, they don't cost that much less to run, usually using between $20 and $35 worth of electricity over a year. If you have a few smaller refrigerators around the house, it might be more efficient to just have one larger, centrally located model.