Green pea galaxies are a class of rare, compact starburst galaxies that have powerful optical emission line [OIII]$\lambda$5007. They are the best low-redshift analogs of high-redshift (z$>$2) Lyman-alpha emitting galaxies (LAEs). They provide unique opportunities to study physical conditions in high-redshift LAEs in great detail. In this dissertation, a few physical properties of green peas are investigated. The first study in the dissertation presents star formation rate (SFR) surface density, thermal pressure in HII regions, and a correlation between them for 17 green peas and 19 Lyman break analogs, which are nearby analogs of high-redshift Lyman break galaxies. This correlation is consistent with that found from the star-forming galaxies at z $\sim$ 2.5. In the second study, a new large sample of 835 green peas in the redshift range z = 0.011 -- 0.411 are assembled from Data Release 13 of the Sloan Digital Sky Survey (SDSS) with the equivalent width of the line [OIII]$\lambda$5007 $>$ 300\AA\ or the equivalent width of the line H$\beta$ $>$ 100\AA. The size of this new sample is ten times that of the original 80 star-forming green pea sample. With reliable T$_e$-based gas-phase metallicity measurements for the 835 green peas, a new empirical calibration of R23 (defined as ([OIII]$\lambda$$\lambda$4959,5007 + [OII]$\lambda$$\lambda$3726,3729)/H$\beta$) for strong line emitters is then derived. The double-value degeneracy of the metallicity is broken for galaxies with large ionization parameter (which manifests as log([OIII]$\lambda$$\lambda$4959,5007/[OII]$\lambda$$\lambda$3726,3729) $\geq$ 0.6). This calibration offers a good way to estimate metallicities for extreme emission-line galaxies and high-redshift LAEs. The third study presents stellar mass measurements and the stellar mass-metallicity relation of 828 green peas from the second study. The stellar mass covers 6 orders of magnitude in the range 10$^{5}$ -- 10$^{11}$ M$_{\odot}$, with a median value of 10$^{8.8}$ M$_{\odot}$. The stellar mass-metallicity relation of green peas is flatter and displays about 0.2 - 0.5 dex offset to lower metallicities in the range of stellar mass higher than 10$^{8}$ M$_{\odot}$ compared to the local SDSS star-forming galaxies. A significant dependence of the stellar mass-metallicity relation on star formation rate is not found in this work.