Mobility and noise are two important issues for electronic devices, and they have many new features in one-dimensional (1D) doped nanostructures. For the convenience of readers the background of solid state physics is reviewed first, and then the transport process in 3D crystal material is introduced. Velocity saturation is an important phenomenon in modern electronic devices, and it is analyzed in an intuitive approach. It is predicted FinFET will be the next generation MOSFET, and its structure and characteristics are introduced. With the reduction of device dimensions the mesoscopic phenomena begin to show up. A simple way to treat transport problem in this domain is the Landauer-Büttiker formula, and the basic equation is derived. Finally the 1D quantum wire structure grown from a bottom-up approach is reviewed. Owing to the good material quality the scattering is very weak, and the wave properties of the coherent transport are discussed. Engineering applications of nanostructures in electronic information processing that manipulates time varying signals often involve device characterizations in the time domain. Since carrier transport in nanostructures is inherently a random process and it causes random fluctuations in quantities like current and voltage, so background knowledge in the microscopic origins of noise and other related practical issues is important to identify enough noise margins for reliable system design. This subject is the focus of the second part of the review article.