**Abstract: **
An estimation of an quantum state or process belongs to nontrivial problems of the quantum theory of measurement. Statistical formulation of the problem using maximum likelihood enables to distinguish between quantum states or to reconstruct a quantum state based on measured data. The estimate may concern also a process transforming quantum states as in the case of quantum logical gates in quantum computing and information processing. The general formulation makes it possible to apply the method to various physical systems, for example, to polarization or spatial states of light.