Doped semiconductor systems have for decades provided an excellent platform to study novel concepts in solid state physics such as quantum hall effect, metal-to-insulator transition (MIT), weak localization and many body interaction effects. Doped Si, in particular and doped Ge has been studied extensively to study MIT as a function of dopant concentration or uniaxial stress. Spin transport phenomena have also been probed in bulk doped Si. All the previous studies involved bulk doped semiconductors where the dopants are spread through the bulk of the material. However spatial confinement of dopants in one or more dimensions may lead to a range of exotic quantum phenomena such as an absence of Anderson localization in one and two dimensions, hole-mediated (Nagaoka) ferromagnetism and new modes of quantum transport, when the Fermi energy lies at or close to centre of the band. Since many of these phenomena are inherent to lower dimensions, it has been hard to observe these experimentally in bulk doped crystals of Si and Ge. Recent advances in the monolayer doping techniques with atoms that closely pack on a surface, has made it possible to design a new class of 2D electron systems (2DES) in elemental semiconductors, such as Si and Ge, where the dopant (P) atoms are confined within a few atomic planes. The uniqueness of these systems lies not merely in the planar doping profile in bulk semiconductors that allow versatile designs of nanodevices, such as 1D wires, tunnel gaps and quantum dots, but also that it is now possible to study the interplay of wavefunction overlap and commensurability effects in 2D with unprecedented control. From an application perspective as well these systems are technologically important as they are aimed at being the building blocks of a solid state quantum computer. This thesis deals with investigating the electrical transport properties, both average (resistance) and dynamic (noise) of doped semiconductor systems in 2D delta layers, 1D wires and 0D quantum dots. We find that the 2D δ-layers shows suppressed low frequency noise and the Hooge parameter of delta doped Si is about five to six orders of magnitude lower when compared to bulk doped Si in metallic regime. At low temperatures, the noise arises in these systems due to universal conductance fluctuations. For 1D wires as well we find that the Hooge parameter is one of the lowest among various 1D systems including carbon nanotubes. We identify that charge traps in the Si/SiO2 are responsible for causing noise in δ-doped systems. Then we study the noise and transport in 2D delta layers as a function of doping density (and hence carrier density and interaction). Weak localization corrections to the conductivity and the universal conductance fluctuations were both found to decrease rapidly with decreasing doping in the Si:P and Ge:P delta layers, suggesting a spontaneous breaking of time reversal symmetry driven by strong Coulomb interactions. At low doping density we observe metal-like dependence of resistance on temperature at low temperatures, raising the possibility of a metallic ground state in 2D at 0 K in doped semiconductors. Finally we probe the low density devices (with broken time reversal symmetry) using superconducting Al as ohmic contacts. Anomalous increase in resistance below the superconducting transition temperature of Al and magnetoresistance with a sharp peak at 0 T is observed. Additionally we find that when the Al is superconducting, there exists a non-local resistance in low doped devices.