Atomically thin 2D materials have gained the interest of the scientific community in the past decade due to their exotic electronic and optoelectronic properties, thus emerging as potential candidates for the next generation of nano-devices. Quantum confinement in one of the dimensions is the primary reason for these exotic properties. However, it has been seen that these properties are widely inconsistent, and they are controlled by variety of factors such as material synthesis, device fabrication, testing environment, etc. Due to low dimensional nature of these materials, defects are inevitable. These defects typically originate from either the presence of bulk impurities or interface between sample and substrate. These defects manifest as mid-gap states in semiconductor channel and act as trapping centers for charge carriers, thus often referred to as trap states. The presence of trap states is not necessarily a detrimental thing. In this dissertation, I will focus on the role these trap states play in the emergence of a few electronic and optoelectronic properties.High responsivity (R) in photodetectors based on 2D materials is mainly associated with a presence of photogating effect in which trap states dynamics plays a crucial role. Photogating also results in fractional power (γ) dependence of the photocurrent (Iph) on an effective illumination intensity (Peff). Chapter 2 presents photoconductivity studies of few layers of rhenium diselenide (ReSe2) based field-effect transistors (FETs) over a wide range of applied gate voltages (-48 V ≤ Vg ≤ 60 V) and temperature (20 K ≤ T ≤ 300 K). A very high responsivities ≈ 16500 A/W and external quantum efficiency (EQE) ~ 106 % (at 140 K, Vg = 60 V and Peff = 0.2 nW) was obtained. Investigating R and γ at various gate voltages and over a wide range of temperatures leads to a strong correlation between R and γ. Such correlations indicate the importance of trap states and photogating in governing high responsivities in these materials. It is expected that thicker samples will aid in photoconduction by effectively increasing photon absorption. In chapter 3, a layer dependent study of optoelectronic properties of indium selenide (InSe) based FETs shows that responsivity decreases for thicker InSe devices. In these devices, photogating remains constant (similar γ) and responsivity depends predominately upon field-effect mobility (μFE). Interlayer resistance regulates the mobility and (consequentially) responsivity. Thus, mobility dominates the responsivity and trap states play second fiddle. The presence of metal−insulator transition (MIT) in two-dimensional (2D) systems leads to tunable material properties by regulating parameters such as charge carrier density. Chapter 4 shows our observation on MIT in the 2D copper indium selenide (CuIn7Se11) flakes by electrostatic doping via the SiO2 back gate. A temperature and gate voltage dependence of conductivity (σ) of CuIn7Se11 FET shows clear evidence of the metallic and insulating phase. Evidence of 2D variable-range hopping (VRH) and percolation critical conductivity confirms the presence of charge density inhomogeneity originating from trap states. The low effective mass and high dielectric of copper indium selenide systems result in a lower critical charge carrier density required for percolation-driven MIT, attended by conventional SiO2 dielectric gate. Even though findings reported in this dissertation are performed on specific materials, fundamental understandings can be easily extrapolated to other 2D systems. Understanding the role of trap states will provide valuable insights for the design and development of high-performance devices using 2D materials.