We discuss the core principles underpinning the concept of identifiability, providing an overview of relevant literature concerning this phenomenon within the domain of complex networks. We delve into the potentialities and inherent constraints associated with the analysis of identifiability in real networked systems. Through this exploration, we establish a comprehensive classification scheme for network identifiability, distinguishing i) structural, ii) functional, and iii) meta-identifiability categories. We explain the principal conceptual distinctions characterising each category. Finally, we deliberate upon the contextual frameworks where system identifiability can be achieved, also highlighting the factors that impede structural, functional, and meta-identifiability.