The atmosphere of the earth restricts the resolution of conventional astronomical imaging to about 1 arcsec. Much higher resolution can be obtained by speckle methods. The Knox-Thompson method and the speckle masking method (bispectrum or triple correlation processing) yield diffraction-limited images in spite of image degradation by the atmosphere and by telescope aberrations. For example, with a 3.6-m telescope a resolution of 0.03" can be obtained at a wavelength of 400 nm. The limiting magnitude is about 18. We will discuss the theory and applications of speckle masking. High-resolution images and simultaneously the spectrum of each resolution element can be obtained by objective prism speckle spectroscopy and projection speckle spectroscopy methods. Finally, we will discuss the application of speckle masking to coherent arrays of telescopes. For example, observations with the 4x8-m ESO VLT can yield the fantastic angular resolution of about 2milli-arcsec.