The paper deals with identifiability and observability of anaerobic digestion (AD) processes. In such kind of processes, generally carried out in continuously stirred tank bioreactors, the organic matter is depolluted by microorganisms into biogas and compost in the absence of oxygen. The biogas is an additional energy source, which can replace fossil fuel sources. The differential algebraic approach of general observation problems has been applied to investigate the identification and observation of a simple AD model. The major discovery is that the biomass specific growth rate can be stably estimated from easily measured quantities: the dilution rate and the biogas flow rate. Next if the yield coefficients are assumed known then, of course, the biomass concentration is observable. Unfortunately, even under the latter strongest assumption the substrate concentration is not observable. This concentration becomes observable if an additional model, say the Monod model, is assumed for the specific growth rate. Illustrative simulations are presented.