Interest on monolayer semiconductors is rapidly growing in recent years. One of the prominent members is hexagonal boron nitride (h-BN). At room tem-perature, it harbors an environment similar to semiconductor vacuum for point defects which is crucial for stable and controllable spin states. This qualification makes h-BN a suitable medium for quantum technological applications. First-principles calculations are essential in order to characterize such systems. Density functional theory (DFT) is one of the most reliable methods used for these type of calculations. Recently, a variant called as DFT-1/2, has been proposed to calculate the band gaps of the materials more accurately without a significant additional computational cost. In the first part of thesis, we have compared the results of DFT and DFT-1/2 for carbon impurities (CB, CN ), single vacan-cies (VB, VN ), double vacancy (divacancy) and Stone-Wales defect in monolayer h-BN. Subsequently, results from computationally expensive techniques such as hybrid or GW are presented and compared with the obtained DFT-1/2 results. Especially for the defect states seemingly hidden in valence or conduction band, DFT-1/2 technique is instrumental in revealing these states while widening the band gap. Thus, we recommend the DFT-1/2 method for a quick screening of candidate band gap defect states. Another outstanding group of semiconductors is transition metal dichalco-genides (TMDs). They owe their advantages to optically addressable valley and bringing optics and mechanics together as in valleytronics, thanks to their high flexibility. In the second part of this thesis, ten TMDs including their janus coun-terparts (JTMDs), namely, MoS2, MoSe2, MoTe2, WS2, WSe2, WTe2, MoSSe, MoSeTe, WSSe, and WSeTe have been computationally studied. To begin with, the electronic band structure of the specified materials have been computed using DFT followed by hybrid calculations over these, with the addition of spin-orbit coupling. Biaxial and uniaxial strain calculations are subsequently performed. JTMDs were previously proclaimed to have a good piezoelectric characteristic. According to our DFT results, JTMDs exhibit band structure and electronic properties in between its constituent TMDs, and in this respect they do not dis-play an outstanding behaviour. Based on the acquired DFT data, spinless and spinful k · p parameters are extracted by fitting around optically active K valley. With the help of k·p parametrization, linear and circular dichroic behaviours are studied for unstrained and strained cases. In consideration of all these materials, WTe2 displays the largest linear dichroic responsitivity for uniaxial strain, since it has the smallest band gap and the greatest uniaxial deformation potential at the K valley. Thus, we propose monolayer WTe2 membranes to be considered for optical polarization based strain measurements, as well as, strain adjustable optical polarizers.