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The review describes the noise properties of the high temperature superconducting (HTS) bolometers developed for the applications in the optical electronic devices of infrared and submillimeter wave-lengths. The principle of high-T_c transition edge bolometer operation and bolometer noise theory are considered, taking into account the peculiarities of constant bias current and constant bias voltage modes. The published results of bolometer noise modeling are discussed. Various sources of the excess 1/f-noise in HTS films as temperature sensitive element for bolometer are reviewed, including the experimental data and modern noise models. Comparative analysis of noise characteristics of the most developed HTS bolometers for application (antenna-coupled microbolometers and bolometers based on silicon micromachining technology) is reported.