Embedded systems have become an essential aspect of our professional and personal lives. From avionics, transport and telecommunication systems to general commercial appliances such as smart phones, high definition TVs and gaming consoles; it is difficult to find a domain where these systems have not made their mark. Moreover, Systems-on-Chips (SoCs) which are considered as an integral solution for designing embedded systems, offer advantages such as run-time reconfiguration that can change system configurations during execution, depending upon Quality-of-Service (QoS) criteria such as performance, energy levels etc. This article deals with aspects related to modeling of these configurations, useful for describing various states of an embedded system, from both structural and operational viewpoints. Our proposal adapts a high abstraction level approach based on the principles of Model-Driven Engineering (MDE) and takes into account the UML MARTE profile for modeling of real-time and embedded systems. Elevating the design abstraction levels help to increase design productivity and achieve execution platform independence, among other advantages. The article details the current proposition of configurations in MARTE via some examples, and points out the advantages as well as some limitations, mainly concerning the semantic aspects of the defined concepts. Finally, we report our experiences on the modeling of an alternate notion of configurations and execution modes within the MARTE compliant Gaspard2 SoC Co-Design framework that has been successful for the design as well as implementation of FPGA based SoCs.