We live in an era where more and more tasks, once thought to be impregnable bastions of human intelligence, succumb to AI. Are we at the cusp where ASR systems have matched expert humans in conversational speech recognition? We try to answer this question with some experimental evidence on the Switchboard English conversational telephony corpus. On the human side, we describe some listening experiments which established a new human performance benchmark. On the ASR side, we discuss a series of deep learning architectures and techniques for acoustic and language modeling that were instrumental in lowering the word error rate to record levels on this task.