During its use, an SSL objects passes several states. The state is internally maintained. Querying the state information is not very informative before or when a connection has been established. It however can be of significant interest during the handshake.
When using non-blocking sockets, the function call performing the handshake may return with SSL_ERROR_WANT_READ or SSL_ERROR_WANT_WRITE condition, so that SSL_state_string[_long]() may be called.
For both blocking or non-blocking sockets, the details state information can be used within the info_callback function set with the SSL_set_info_callback() call.