Since the discovery the submillimeter galaxy population was made nearly 10 years ago using the single-dish JCMT, we have learned a great deal about these galaxies. Radio identification and spectroscopic followup have shown that these galaxies are the dominant star former at intermediate redshifts of z~2-3 and they generally do not overlap with rest-frame UV identified high-redshift galaxies (ie, Lyman-break galaxies). This implies that the sources of the cosmic submillimeter background has been missed by optical observations and they are a cosmologically important population. However, from the COBE/DIRBE experiment, we also learn that the radio-identified submillimeter galaxies only contribute ~20% to the total submillimeter background, and the sources of the rest 80% of the background are still poorly understood. Because of their faintness in the radio and submillimeter, systematic studies of these sources will only be possible with next-generation instruments such as the EVLA and ALMA. However, it is possible to study a small sample of such sources using existing instruments. In this talk, I will summarize our ongoing efforts in understanding the bulk of the submillimeter background. We use interferometers in the radio (the VLA) and submillimeter (the SMA) to study sources previously not detected by single-dish submillimeter telescopes, sometimes with the help from lensing of massive clusters. We now have good evidence that the bulk of the submillimeter background arises from faint sources at low redshifts of z~1. We also see evidence that hyper-luminous submillimeter sources exist at z>4. These show that submillimeter galaxies are cosmologically important over a broad redshift range.