Characterized by ultra-fast and arc-free fault clearing, solid state circuit breakers (SSCBs) are getting increasing popularity with the latest development of advanced power semiconductor devices, like the silicon carbide (SiC) MOSFETs. On the other hand, the mature and cost-effective thyristor technology exhibits the beneficial features of low conduction losses, high surge current capability, bidirectional voltage blocking capability, etc., making it a very attractive candidate for SSCB development. However, the conventional thyristors (silicon controlled rectifiers) have no current turn-off capability and need some auxiliary circuits (e.g. LC resonant circuit) or special topology (e.g. Z-source breakers) to be applied in SSCBs. Meanwhile, some active turn-off thyristors (like integrated gate-commutated thyristors, emitter turn-off thyristors, etc.) are specially modified to have current turn off capability, and better suitable for SSCBs. This paper reviews and studies the SSCBs based on the conventional or active turn-off thyristors. The design challenges and performance comparison of SSCBs with different thyristor technologies are also discussed.