A split-cycle internal combustion engine (ICE) is provided, comprising a compression cylinder, an expansion cylinder and a crossover valve having a valve cylinder housing inside a shuttle and a combustion chamber structure defining a combustion chamber. The shuttle is configured to perform reciprocating motion inside the valve cylinder synchronously with a compression piston and an expansion piston, thereby alternatingly fluidly coupling and decoupling the combustion chamber with the compression cylinder and with the expansion cylinder, selectively. Sealing rings positioned between the valve cylinder and the shuttle prevent gas leaks between them during the reciprocating motion. In some embodiments, a phase shift between the pistons may be set or varied by a piston phase transmission gear. A bi-directional fluid flow split-cycle internal combustion engine (ICE) is also provided having a first cylinder, a second cylinder, a combustion chamber and a single crossover valve fluidly communicating them. A three-cylinders split-cycle internal combustion engine (ICE) is also provided, having a compression cylinder and a combustion chamber, wherein a single crossover valve alternatingly fluidly couples the combustion chamber to two or more expansion cylinders.