Dissipative solitons are self-localized structures resulting from a double balance between dispersion and nonlinearity as well as dissipation and a driving force. They occur in a wide variety of fields ranging from optics, hydrodynamics to chemistry and biology. Recently, significant interest has focused on their temporal realization in driven optical microresonators, known as dissipative Kerr solitons. They provide access to coherent, chip-scale optical frequency combs, which have already been employed in optical metrology, data communication and spectroscopy. Such Kerr resonator systems can exhibit numerous localized intracavity patterns and provide rich insights into nonlinear dynamics. A particular class of solutions consists of breathing dissipative solitons, representing pulses with oscillating amplitude and duration, for which no comprehensive understanding has been presented to date. Here, we observe and study single and multiple breathing dissipative solitons in two different microresonator platforms: crystalline MgF2 resonator and Si3N4 integrated microring. We report a deterministic route to access the breathing state, which allowed for a detailed exploration of the breathing dynamics. In particular, we establish the link between the breathing frequency and two system control parameters - effective pump laser detuning and pump power. Using a fast detection, we present a direct observation of the spatiotemporal dynamics of individual solitons, revealing irregular oscillations and switching. An understanding of breathing solitons is not only of fundamental interest concerning nonlinear systems close to critical transition, but also relevant for applications to prevent breather-induced instabilities in soliton-based frequency combs.