The migration of network functions (NFs) into virtualized network infrastructures brings significant benefits to enterprise networks, while creating opportunities for new cloud service models (i.e., NF-as-a-Service). Network service embedding (NSE) entails serious challenges, stemming from middle-box policies prescribed by network operators and the implications of NFs on network traffic (i.e., bandwidth conservation or traffic amplification) that complicate the estimation of bandwidth demands. The NSE problem is further exacerbated by the location dependencies of certain NFs, which, in conjunction with the limited geographic footprint of NF providers, raise the need for network service mapping across multiple providers. In this paper, we present a holistic approach to multi-provider NSE. We introduce a new service model that simplifies the specification of network service requests and the estimation of bandwidth demands. We further define topology abstractions tailored to NSE that are exposed to a network service composition layer (NSCL), interposed between the clients and the NF providers. Based on this service model and topology abstractions, we propose Nestor, a system that generates efficient network service embeddings via network graph rendering, request partitioning among datacenters (DCs), and request segment mappings onto DC networks.