The recent discoveries of topological insulators (TI) has opened a new realm for study¬ing topological systems and exploring the exotic properties they offer. The in-built topological protection against direct backscattering and absence of localization makes two-dimensional (2D) surface states of bismuth chalcogenide-based strong TI a promising platform for studying interesting phenomena in condensed matter physics like dissipation-less transport, quantum anomalous hall effect, topological magnetoelectric effect, majo¬rana fermions etc. and also makes this system very suitable for applications in the fields of electronics and spintronics. However, realization of these novel states can be difficult because of scattering of surface states from different types of disorders (intrinsic or ex¬trinsic) or the presence of parallel channels in the bulk of the sample which can dominate over surface transport. The main goal of this thesis is to evaluate the performance of TI as an electronic element and look into elastic and inelastic scattering processes and kinetics of these scatterers. In most part of this work we concentrate on the magnitude and origin of low-frequency flicker noise or the 1/f-noise, a key performance marker in electronics, to characterize the electrical transport in TI. In this work we have studied 1/f-noise in both mechanically exfoliated TI-flakes and epitaxially grown TI films by varying chemical potential and temperature. Our study of exfoliated TI-flakes with a wide range of thickness (10 nm to 80 μm) suggests that whereas at thinner (<100 nm) samples and at low temperature (<70 K), the electrical transport happens entirely at the surface, resistance fluctuations in the surface states are mainly caused by potential fluctuations caused by generation-recombination processes in the bulk of TI. Study of 1/f-noise in MBE-grown magnetically doped TI reveals signature of hopping transport through localized bulk mid gap states. These states can either be Cr-impurity band or disorder-induced mobility edge states of bulk valence band. Our study of quantum transport in exfoliated TI-devices indicate presence of a de-coherence mechanism which saturates phase-coherence length and temperature below T< 3 K and results from a unique scattering mechanism caused by localized magnetic moments in these systems