Sensing Technology (ST) plays a key role in Structural Health-Monitoring (SHM) systems. ST focuses on developing sensors, sensory systems, or smart materials that monitor a wide variety of materials’ properties aiming to create smart structures and smart materials, using Embedded Sensors (ESs), and enabling continuous and permanent measurements of their structural integrity. The integration of ESs is limited to the processing technology used to embed the sensor due to its high-temperature sensitivity and the possibility of damage during its insertion into the structure. In addition, the technological process selection is dependent on the base material’s composition, which comprises either metallic or composite parts. The selection of smart sensors or the technology underlying them is fundamental to the monitoring mode. This paper presents a critical review of the fundaments and applications of sensing technologies for SHM systems employing ESs, focusing on their actual developments and innovation, as well as analysing the challenges that these technologies present, in order to build a path that allows for a connected world through distributed measurement systems.