Optical frequency combs are optical sources, which spectrum consists of a series of equally spaced narrowband frequencies. They made an outstanding leap forward in the accuracy of optical frequency metrology and became an attractive tool for numerous applications including optical atomic clocks, fast telecommunications, astronomy, molecular spectroscopy, and microwave and optical waveform synthesis. Discovered in 2007, microresonator-based frequency combs (also Kerr combs) have become a breakthrough in the field by enabling the optical comb generation from a continuous-wave laser via nonlinear parametric frequency conversion effects enhanced within a high-quality microresonator. Kerr combs attracted significant attention due to their ability to operate in a soliton regime when self-sustaining optical pulses – dissipative Kerr solitons - are formed in the microresonator relying on a double balance between the dispersion and nonlinearity of the system as well as cavity losses and the gain from the driving laser. Dissipative Kerr solitons allow access to broadband, coherent optical combs with large repetition rates from microwave to terahertz domains, which can be generated from chip-scale microresonators. Due to compactness and unprecedented performance, such soliton-based Kerr combs represent a promising solution for a variety of real-world optical comb applications, which has been demonstrated over the last four years. In this thesis, several aspects of dissipative Kerr soliton dynamics are investigated in integrated silicon nitride microresonators. The results include the first experimental study of the Raman-induced self-frequency shift in dissipative Kerr solitons, the discovery and explanation of the soliton switching phenomenon, which enables controllable successive elimination of soliton pulses from a microresonator, the experimental observation of breathing soliton states as well as the demonstration of collectively-ordered soliton ensembles – perfect soliton crystals. The results are universal across other soliton generating platforms. Apart from elucidating basic dynamical properties of dissipative Kerr solitons, they contribute to the understanding of soliton behavior in the presence of high-order nonlinear, dispersion and thermal effects in real systems. Besides the study of the soliton dynamics, probing and manipulation techniques for dissipative Kerr solitons are developed. They enable deterministic soliton switching and controllable access to application-relevant single soliton states. The techniques also allow for non-destructive monitoring of key soliton parameters and controllable soliton state translations in the parameter space of the driven microresonator system. The developed understanding and control of soliton states are used to demonstrate dissipative Kerr solitons operating at 1 um wavelength and covering the biological imaging window. Furthermore, in collaboration with KIT soliton-based combs generated in silicon nitride microresonators are employed for massively parallel optical coherent communications and ultrafast optical ranging, where the record performance of DKS states in both applications has been demonstrated. Lastly, a rack-mountable standalone system for the DKS generation, which can be readily used outside of the laboratory environment, is developed, tested and is employed in first experiments on optical circuit switching for data centers and all-optical convolution neural networks.