There are four basic types of flexible circuits, varying in degrees of complexity. These three types of circuits can be used in different combinations to solve most every interconnection design problem.
The simplest circuits are single-sided flexible circuits. They provide maximum flexibility for dynamic applications and can withstand hundreds of millions of flex cycles These simple circuits are also the most easily adaptable to SMT, TAB, and other developments in circuit technology.
Double-sided circuits are somewhat limited in their capacity to flex because of a thicker, more complex level of design. The ability to interconnect between sides using through-hole plating helps double-sided circuits carry complex designs, and still maintain flexibility
Multilayer circuits are ideal for complex, highly populated design requirements. Large numbers of conductors can be designed into a small package. Flexibility may be somewhat limited, de pending on the number of layers in the design. These multi-layer circuits are ideal for rigid/flex designs, combining a multilayer flex circuit with a hard board.
Multilayer circuits are the ideal problem-solving technology when confronted with design challenges like unavoidable crossovers, specific impedance requirements, elimination of crosstalk in sensitive circuits, additional shielding or ground planes, and high component density.
Rigid-Flex circuits are circuits combination of Rigid circuit and Flex circuits. So it have both the advantage of each other and it's newest types used in various applications.