  Observability is a modelling property that describes the possibility of
inferring the internal state of a system from observations of its output. A
related property, structural identifiability, refers to the theoretical
possibility of determining the parameter values from the output. In fact,
structural identifiability becomes a particular case of observability if the
parameters are considered as constant state variables. It is possible to
simultaneously analyse the observability and structural identifiability of a
model using the conceptual tools of differential geometry. Many complex
biological processes can be described by systems of nonlinear ordinary
differential equations, and can therefore be analysed with this approach. The
purpose of this review article is threefold: (I) to serve as a tutorial on
observability and structural identifiability of nonlinear systems, using the
differential geometry approach for their analysis; (II) to review recent
advances in the field; and (III) to identify open problems and suggest new
avenues for research in this area.
