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Much research has been dedicated to methods that estimate the available bandwidth in a network from traffic measurements, yet little progress has been made on achieving a foundational understanding of the bandwidth estimation problem. In this talk, we develop a min-plus system theoretic formulation of bandwidth estimation. We show that the problem as well as previously proposed solutions can be concisely described and derived using min-plus system theory, thus establishing the existence of a strong link between network calculus and network probing methods. We relate difficulties in network probing to potential non-linearities of the underlying systems, and provide a justification for the distinctive treatment of FIFO scheduling in network probing. Experiments on an Emulab testbed are used to evaluate the theoretical concepts in actual implementations of probing schemes.