CVD technology for homoepitaxial growth of single-crystal diamond has been experiencing serious difficulties for more than ten years. Long-term morphologically stable epitaxy of a crystal is impossible: as the crystal grows, a surface relief develops; over time, the appearance of polycrystals on the growth surface is inevitable, overgrowth of a polycrystalline "rim" along the edges, and the structural perfection of the material is not achieved. Productive epitaxy on {111} faces is impossible due to inevitable twinning. An achievement is considered to be the growth of 1÷2 mm of epitaxial material in one session on a well-prepared face vicinal to (001). To noticeably grow a crystal, one has to periodically remove it from the reactor, cut off the polycrystalline "rim" around the perimeter and repolish the growth surface for a new growth session. The great prospects for using CVD diamond have so far been realized very little. There is a need to overcome these problems. It became clear that the structural perfection of a material is inextricably linked to the achievement of morphologically stable epitaxial growth. A layer growth model was used to analyze the growth mechanism of single-crystal CVD diamond. On its basis, such key components of the growth surface as sources of layered growth and a staircase of growth steps are described. The main reasons for the morphological instability of layer growth are: a) positive feedback due to the action of a boundary diffusion layer with a large concentration gradient of growth radicals; b) Ehrlich–Schwoebel barrier for the movement of adatoms over the edge of the growth step. The main manifestations of morphological instability of homoepitaxial diamond growth include step bunching (with the formation of macrosteps), meandering of steps, growth of hillocks and mounds, and formation of growth pits. It is shown that these destructive phenomena arise and develop during epitaxy on faces close to {100}. The development of the growth surface topography inevitably leads to the appearance of twins on it, that is, epitaxy failure. The diagnosis of morphological instability of diamond epitaxy by CVD method made it possible to put forward proposals for overcoming it. These include: a) creating controlled sources of layered growth; b) preparing a staircase of growth steps by properly polishing the growth surfaces; c) selection of the optimal vicinal angle of growth surfaces; d) selection of supersaturation conditions for the morphologically stable functioning of sources of layer growth and development of growth layers.