Galaxies are fundamental building blocks of the Universe. Understanding their detailed formation and evolution is a major task in modern astronomy. Star formation is a key process that regulates galaxy formation and evolution. A consistent picture is emerging from modern galaxy surveys, whereby the star formation rate density peaks at $z\sim2$, and exponentially declines to the present day. Systematic study of star-forming galaxies at the peak epoch holds the key to our understanding of galaxy formation and evolution. Chapters 2 and 3 of this dissertation present our studies based on the narrow-band imaging techniques. In Chapter 2, we present the results from the dual narrow-band imaging surveys in the search of Lyα and Hα emitters at the same redshift ($z=2.24$) and in the same field (Extended Chandra Deep Field South). We estimate the mean Lyα escape fraction at $z=2.24$ by comparing the observed ratio between the Lyα luminosity to total luminosity and to the extinction-corrected Hα luminosity fraction. We find that: (1) the difference in the dust attenuation between ionized gas and stellar continuum increases with star formation rate; (2) there is an anti-correlation between Lyα escape fraction and dust attenuation; (3) the global Lyα escape fraction at $z=2.24$ is (3.7pm1.4)%; For the first time we point out that different extinction corrections significantly affect the studies of high-redshift star-forming galaxies. In the second project presented in this dissertation, we use the narrow-band-selected emission-line galaxies to identify the protoclusters, and map the cosmic structure around them in the early universe. Our preliminary results show that: (1) comparing to the random field, the galaxy overdensity in our two overdense fields BOSS (Baryon Oscillation Spectroscopic Survey) 1244 and BOSS1542 is $\delta_g\geqslant 11$; (2) a large-scale filamentary structure is shown by the Hα emitters in the BOSS1542. The extremely luminous infrared galaxies contributed almost half of the cosmic star formation at the epoch of the peak star formation. In our third and forth projects, we study the physical properties of this extremal galaxy extreme population through the submillimeter observations. We develop a machine-learning method to identify the possible multi-wavelength counterparts of submillimeter detected source in panoramic, single-dish submillimeter surveys using a training set constructed from higher angular resolution interferometric submillimeter observations. The results show that: (1) the recovery rate and precision of the developed machine-learning method are (77.2pm4.7)% and (82.0pm4.9)%, respectively, and the recovery rate of Submillimeter Galaxies (SMGs) reaches to 85% if we combine the radio identifications; (2) the self-test of the training set and a set of independent tests confirm the robustness of our method; (3) our analysis based on the stacked images demonstrates that the method can recover faint and/or diffuse submillimeter galaxies even if they are below the detection threshold of interferometric observations. These results mean that we have efficiently reduced the uncertainties in the follow-up studies of submillimeter sources resulting from the coarse angular resolution of single-dish submillimeter surveys. Our project is the first application of machine-learning techniques in the studies of submillimeter galaxies. We apply this method to the recent single-dish submillimeter survey in the Cosmic Evolution Survey (COSMOS) field (S2COSMOS). About 1200 optical/near-infrared/radio counterparts of submillimeter galaxies have been identified. We study the multi-wavelength properties of submillimeter galaxies based on these precisely identified counterparts. We confirm that these identified counterparts to single-dish submillimeter sources represent the complete physical properties of submillimeter galaxies, i.e., they tend to lie at higher redshift and they are undergoing massive bursts of star formation at rates of $\geqslant 10^{2}M_{\odot}$cdot yr^-1. We also apply our method to the whole COSMOS field and identify sim9000 likely optical/near-infrared counterparts of submillimeter galaxies, which are below the detection limit of single-dish submillimeter observations. We can investigate the evolutionary connections between submillimeter galaxies and other populations at the same epoch or in the lower-redshift Universe by comparing their clustering strength, which reflect their underlying dark matter distributions. Our studies provide more accurate constraints on galaxies formation and evolution models, particularly for the massive ones.