Recent rapid advancements in wide and deep surveys at millimeter and submillimeter (mm and submm) wavelengths have led to successive discoveries of numerous mm/submm-bright galaxies (SMGs), i.e., dusty extreme starburst population in the early universe. They contribute significantly to the cosmic star formation rate density at z > 1, and evolutionally links to bright quasars and the most massive giant elliptical galaxies have also been suggested. After brief overview of the mm/submm deep surveys to date, characteristics of deep surveys at mm/submm waveband is discussed; the ground-based long-wavelengths (~1 mm) deep surveys are complementarly to short-wavelengths submm surveys with Herschel in order to address the redshift distribution of dusty starburst galaxies. Some recent hot issues of SMGs are also described, including discovery of ultra-bright population, the origin of extreme starburst in SMGs, discovery of a protoquasar-like SMG in the core of a protocluster, and a quest for high-redshift (z > 4) SMGs.