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Hysteresis does not vanish in materials essentially free from defects and domain wall pinning. It arises from the existence of many geometrically different domain structures separated by intrinsic energy barriers. Although generally metastable, these states can nevertheless be explored by suitable excursion in the manifold of domain structures, along which irreducible irreversibility is present. This idea is illustrated by experiments performed on garnet layers with uniaxial anisotropy (bubble material). Cooling the layer from T>Tc in a field H normal to it results in various states: parallel stripes (H=0), bubbles of increasing diameters and mixtures of bubbles and stripes (H<52 Oe), and mazes of convoluted stripes with defects (forks, dead ends). Cycling the applied field at constant temperature also causes evolution of the structure. For example, starting from parallel stripes the structure evolves toward a maze with intermediate steps corresponding to stripe folding, and then there is the onset of defects (forks, dead ends). We classify these various structures in a kind of phase diagram, depending on the following parameters: current field H, maximum field Hmax previously applied, and memory temperature Tm at which the domain structure is nucleated. The relations and irreversible paths between various structures are precised. We also discuss mechanisms for topological evolution linked with changes in the equlibrium period of the structure. Irreversibility arises from asymmetric processes of domain collapse and nucleation. The first stages in the processes leading from bubbles to stripes, or from parallel stripes to mazes, can be analyzed respectively in terms of elliptical and folding instabilities, the latter being similar to the undulation instability of smectic A liquid crystals.

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