As the main source of slab for hot rolled coil, wide-thick slab, and ultra-thick plate (strip) products, continuous casting slab are mostly produced by vertical arc and arc continuous casters. Micro-alloyed steel containing Ti, Nb, B, Al, V, and other microalloy elements is the main component of steel in companies at home and abroad. It adopts the production process of vertical arc or arc continuous casters. The slab (especially the inner arc) often forms transverse corner crack, resulting in serious quality defects such as edge crack, warping and broken edge in the subsequent rolling process, which restricts the high quality, high efficiency, green and low-cost preparation of micro-alloyed steel plate (strip). This is a common technical problem in the steel industry. This chapter will focus on the formation mechanism of transverse corner crack in conventional and wide-thick slab of micro-alloyed steel, the thermo-mechanical and kinetics of dual-phase particle precipitation in the solidification process of typical microalloy components, the evolution of high temperature structure, the solidification thermo-mechanical evolution of slab in the mold and secondary cooling casting flow and its control. On this basis, the development and application of new crack control technology and device technology based on novel convex-structure mold and corner grain refinement of slab in secondary cooling high temperature zone are introduced.