Modern data-intensive applications are increasingly demanding in terms of non-functional properties such as performance, latency, security, and privacy. In order to achieve such non-functional properties, modern applications benefit from being developed as a composition of services and deployed in a heterogeneous continuum infrastructure that includes Edge and Cloud facilities. In this scenario, the infrastructures used to deploy services play a crucial role in providing or supporting non-functional properties of the applications. For instance, low latency can be achieved via deployment of services in the far edge nodes. Most of the current literature addresses the problem of deployment of single (stateless)services mainly with the aim of ensuring and verifying requirements in terms of resources and performance. Only few solutions exist to deploy applications made of services workflows, and in most of the cases they are focused on functional composition. In general, they fail to address composition deployment preserving advanced non-functional properties such as security and privacy. This thesis proposes novel assurance methodology for modern continuum infrastructures, enabling lightweight in-depth verification and assessment of non-functional properties constituting the key cornerstone for a fully non-functional-aware deployment of service based applications. The thesis proposes an advanced continuum infrastructure, where the 5G MEC is integrated as an Edge node. It also considers a continuum which is empowered with a big data ecosystem of services, where data-intensive analytic workflows can be executed to support critical applications. The assurance methodology defined in the thesis is collaborative and lightweight, and is based on i) transparent collection of evidence representing measurements of relevant continuum states (obtained via monitoring or testing of standard infrastructure-level hooks), ii) aggregation of measurements into metrics and iii) contracts linking metrics to specific non-functional properties. The assurance methodology decouples infrastructure assurance from data processing assurance and application-level assurance. It is the first attempt to suggest that infrastructure and data processing assurance can effectively complement application-level assurance with a limited increase in computational effort while fully applicable in modern continuum infrastructures. The contributions of this thesis are manifold: i) a generic assurance methodology for modern infrastructures ii) a set of specific verticalization of the generic assurance for 5G MEC, Big Data pipelines and CDN networks, iii) a novel notion of continuum empowered by 5G, iv) property aware deployment solution for the continuum integrating assurance controls, v) a complete realization of a continuum infrastructure with simulated 5G nodes and a real data-intensive application for robotic agronomy vi) full experimental evaluation of utility usability and performance. The assurance approaches developed in the thesis have been applied to a real-world scenario through the construction of a complete 5G-enabled Edge-Cloud continuum infrastructure. This was achieved by integrating a 5G network simulator, a MEC deployment infrastructure, a Big Data engine, and a data analysis pipeline platform. This continuum was used to realize a concrete application in the area of IoT-based automated agronomy. Such application is capable of handling the collection, ingestion, analysis and visualization of on-field data. Such complex modern application requires guarantees on a set of advanced non-functional properties that were verified adopting the assurance methodology defined in the thesis. The obtained results demonstrate the utility and usability of the assurance in the context of modern data-intensive application as well as the limited impact in terms of performance obtained thanks to the approach based on infrastructure-level monitoring and lightweight evidence collection.