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Optical frequency combs, which got their name due to characteristic spectra consisting from plurality of narrow equidistant lines, produced a revolution in metrology and high-precision measurements in the last decade. These combs are obtained tradionally with femtosecond mode-locked lasers. However in 2007 a new phenomenon was discovered in nonlinear optics - spontaneous formation of similar Kerr combs in passive dielectric microresonators under continuous wave pump. These microresonator based combs which can be as broad as one octave are formed as a result of multiple and cascaded four-wave-mixing hyper-parametric processes. The report presents the results of recent theoretical and experimental studies demonstrating the possibility to generate broadband coherent combs. Microresonator based Kerr combs open the route to novel compact and efficient photonic devices, namely portable comb sources, ultrastable microwave photonic oscillators and femtosecond pulse generators. This promise is supported by predicted and recently experimentally demonstrated controlled transition from chaotic to phase locked stable combs associated with circulating bright temporal solitons in whispering gallery mode crystalline and integrated ring resonators with anomalous group velocity dispersion. Experimental results are in excellent agreement with theoretical analysis and numerical simulations. Coherent optical frequency combs are also possible in normal dispersion regime with the formation of dark solitons and flat-topped stationary solitonic structures – platicons. These platicons allow more efficient conversion of the c.w. pump to the comb power than bright solitons. Soft excitation of platicons is possible with dispersion engineering, laser injection locking and amplitude modulation of the pump at a frequency corresponding to free spectral range of the microresonator.