Physical and numerical experiments carried out over the past 30+ years suggest that the phenomenon of deterministic chaos is ubiquitous in physical systems. Experience has shown that inference of the mathematical objects (the differential equations, equilibrium measures, Lyapunov exponents, etc.) governing the dynamics of such systems from time series data is a delicate problem even when this data is uncorrupted by noise. Inference from noisy data is therefore bound to be doubly difficult. Although various ad hoc noise reduction algorithms have been proposed (some seemingly effective when tested on computer-generated data from low-dimensional chaotic systems), their theoretical properties are largely unknown. This talk will address the problem of noise removal for time series y_n of the form y_n~=~& x_n~+~e_n x_n~=~&F(x_{n-1})~=~F^n(x_0) where e_n is observational noise, F is a deterministic C^2 mapping with a uniformly hyperbolic attractor LAMBDA, and x_0 is a point on or near LAMBDA. It will be shown that (1) If the noise vectors e_n are i.i.d., mean zero, and uniformly bounded, then consistent estimators of the signal vectors x_n may be constructed, provided the error bound is sufficiently small; but (2) If the noise vectors e_n are i.i.d., mean zero, and Gaussian, then there are no consistent estimators of the signal vectors x_n. Some practical issues connected with these theorems will also be discussed.