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This paper surveys, reviews, and critiques analytic models of MOSFET short-channel effects (SCEs) in subthreshold published over the past four decades. In the first half of this paper, the published models on SCEs are categorized into the following four main groups based on their approach: 1) charging sharing models; 2) empirical expressions; 3) polynomial potential models; and 4) analytic solutions to 2-D Poisson's equation. The strength and weakness of each approach are elaborated in terms of its physical soundness and predictive ability. A key development was the exponential dependence of SCE on channel length (L) , SCE ~ exp(-L/l0), leading to the introduction of scale length (l0). In the second half of this paper, the predictions of each analytic SCE model are examined by generic 2-D numerical simulations. In particular, the merit of each model is judged by its prediction on the scale length (l0) as a function of the thickness and dielectric constant (κ) of the gate insulator. Only one model, i.e., the generalized scale length model that treated the silicon and insulator regions as two distinct dielectric regions with shared boundary conditions, correctly predicted the MOSFET scale length under all dielectric constant and thickness conditions. A variation of the generalized scale length model applies to recent multiple-gate MOSFETs near the limit of scaling.