The present disclosure provides (i) RNA-guided polypeptides (e.g., circular permuted Cas9 proteins) in which the N-terminal end of an N-terminal fragment of a parent RNA-guided polypeptide (e.g., a parent Cas9 protein) is fused (e.g., via linker) to the C-terminal end of the C-terminal fragment (thereby generating new N- and C-termini), (ii) conditionally active RNA-guided polypeptides (e.g., conditionally active circular permuted Cas9 proteins), and (iiii) Cas9 fusion polypeptides that include an internal insertion of a heterologous polypeptide; as well as methods that employ the above polypeptides.