This bachelor thesis deals with the problems of digital image compression. There are described basic color models RGB and YCbCr and conversion between them. Described are currently used codecs for digital images. JPEG compression format is discussed in more detail, which currently is still the most widely used format for digital photos. Described is a process of digitizing the image using the JPEG standard, which includes sampling, quantization and coding. Described are also formats JPEG2000, PNG and WebP. End of chapter are described methods for subjective and objective evaluation of the quality of digital image compression. Among the subjective methods include Double Stimulus Impairment Scale (DSIS) and Double Stimulus Continuous Quality ...