Numerous phenomena in the theory of automatic regulation, mechanics, radiophysics, biology, immunology, economics, robototechnics, etc. need for theiccorrect qualitative and quantitative description to use equations with time lag. One problem which here arises is connected with states estimate of stochastic hereditary systems [1]. This paper is a survey of some results and problems of filtering, interpolation and smoothing for arbitrary Gaussian stochastic processes for the case of linear observations with delays. In particular, the estimate problems of solutions of linear stochastic differential equations with delays and integral equations of Volterra are considered. Besides new method for solution of optimal control problem with incomplete state information is adduced. The survey is based on the papers [2-14]