In the last decade, the massive penetration of Distributed Generators (DGs) has brought significant technical challenges to all the aspects related to the planning and operation of distribution networks. Thus, smart grid concept has evolved as a new operating paradigm replacing conventional approaches that were deployed in passive distribution networks. This new operation framework is equipped with intelligent measurement, communication and control infrastructures enabling an efficient electric power transfer from different point of supplies to the end consumers. This modernization and, at the same time, the ever-increasing utilization of sensitive loads in the industrial, commercial and residential distribution networks implies a higher level of requirement regarding the quality of supply. Availability is the most important factor when it comes to power quality. Therefore, the restoration of distribution systems, considering their new active status, is a timely topic that deserves to be revisited. In this regard, a novel analytical optimization model of the restoration problem is first proposed for passive distribution networks. The considered self-healing actions besides the switching operation are the tap setting modification of voltage regulation devices including I) On-Line Tap-Changing (OLTC) transformers, II) Step Voltage Regulators (SVRs), and III) Capacitor Banks (CBs). Next, the developed formulation is modified and extended such that it is applicable also for active distribution networks. In order to account for the requirements imposed by the start-up process of disconnected DGs, a novel “multi-step restoration” strategy is introduced. For ensuring the feasibility of the obtained solution concerning the technical constraints (e.g. voltage and current limits), a recently published method for the exact and convex relaxation of the Optimal Power Flow (OPF) problem is incorporated into the developed formulation of the restoration problem. In the next step, we propose a solution strategy making the multi-period restoration problem tractable for analytical solvers in case of a grid of realistic size. According to this strategy, the line switching variables and the AC power flow model are decomposed into master and sub problems, which are solved through successive iterations. At each iteration, the solution of the sub problem is used to augment the constraints of the master problem with the proposed feasibility or optimality cuts. The numerical results indicate that the proposed decomposition algorithm provides, within a short time (after a few iterations), a restoration solution with a quality that is close to the proven optimality, when it can be exhibited. In this thesis, along with the network security constraints in steady-state, the transient constraints associated with the starting of induction motor loads are also accounted for in the developed restoration problem. In this regard, an analytical and convex model is derived representing the starting transients of an induction motor in a semi-static fashion. This model is then integrated into a load restoration problem aiming to find the optimal energization sequence of different loads (static and motor loads). We validate the feasibility of the optimization results in terms of these transient operational limits using I) off-line time-domain simulations, and II) a Power Hardware-In-the-Loop experiment.