We consider the problem of online estimation of time-invariant unknown parameters for a linear regression equation (LRE) affected by bounded non-vanishing disturbance with unknown model (e.g., exogenous perturbations and non-factorizable system nonlinearities). Most of its known solutions ensure only uniform ultimate boundedness of parametric error, i.e., robust (biased) parameter estimates, which complicates the application of such approaches to practical scenarios. At the same time, several methods have been proposed that guarantee exact (unbiased) estimation of unknown parameters under mentioned conditions, but such algorithms, unfortunately, have attracted undeservedly little attention from the adaptive control community. The aim of this study is to present a brief overview of such exact methods, which is expected to help to make them more popular. All theoretical properties of the approaches under consideration are validated via numerical experiments.