5G and beyond 5G (B5G) networks are expected to accommodate a plethora of network services with diverse requirements using a single physical infrastructure. Hence, the ``one-size fits all'' paradigm that characterized the 4th generation of wireless networks is no longer suitable. By leveraging the last advent of Network Function Virtualization (NFV) and Software-Defined Networking (SDN), Network Slicing (NS) is considered as one of the key enablers of this paradigm shift. NS will enable the coexistence of heterogeneous services by partitioning the physical infrastructure into a set of virtual networks ''(the slices)'', each running a particular service. Besides, NS offers more flexibility and agility in business operations. Despite the advantages it brings, NS raises some technical challenges. The placement of network slices is one of them, it is known in the literature as the Virtual Network Embedding Problem (VNEP), and it is an NP-Hard problem. Therefore, the first part of this thesis focuses on unveiling the potential of Deep Reinforcement Learning (DRL) and Graph Neural Networks (GNNs) to solve the network slice placement problem and overcome the limitations of existing methods. Two approaches are considered: The first one aims to learn automatically how to solve the VNEP. Instead of putting any constraint on the topology of the physical infrastructure or extracting features manually, we formulate the task as a reinforcement problem, and we use a graph convolutional-based neural architecture to learn how to find an optimal solution. Next, instead of training a DRL agent from scratch to find the optimal solution, a process that may result in unsafe training, we train it to reduce the optimality gap of existing heuristics. The motivation behind this contribution is to ensure safety during the training of the DRL agent. The placement of the slices is not the only challenge raised by NS. Once the slices are placed, monitoring the status of network slices becomes a priority for both network slices' tenants and providers in order to ensure that Service Level Agreements (SLAs) are not violated. In the second part of this thesis, we propose to leverage machine learning techniques and network tomography to monitor the network slices. Network Tomography (NT) is defined as a set of methods that aim to infer unmeasured network metrics using an end-to-end measurement between monitors. We focus on two main challenges. First, on the inference of slices metrics based on some end-to-end measurements between monitors, as well as on the efficient monitor placement. For the inference, we model the task as a multi-output regression problem, which we solve using neural networks. We propose to train on synthetic data to augment the diversity of the training data and avoid the overfitting issue. Moreover, to deal with the changes that may occur either on the slices we monitor or the topology on top of which they are placed, we use transfer learning techniques. Regarding the monitor's placement problem, we consider a special case where only cycles' probes are allowed. The probing cycle schemes have a significant advantage compared to regular paths since the source probe is actually the destination, which reduces the synchronization problems. We formulate the problem as a variant of the Minimum Set Cover problem. Owing to its complexity, we introduce a standalone solution based on GNNs and genetic algorithms to find a trade-off between the quality of monitors placement and the cost to achieve it.