Large language models (LLMs) are the first neural network machines capable of carrying on conversations with humans. They are trained on billions of words of text scraped from the internet. They generate text responses to text inputs. They have transformed the public awareness of artificial intelligence, bringing on reactions ranging from astonishment and awe to trepidation and horror. They have spurred massive investments in new tools for drafting texts, summarizing conversations, summarizing literature, generating images, coding simple programs, supporting education, and amusing humans. Experience with them has shown them likely to respond with fabrications (called "hallucinations") that severely undermine their trustworthiness and make them unsafe for critical applications. Here, we will examine the limitations of LLMs imposed by their design and function. These are not bugs but are inherent limitations of the technology. The same limitations make it unlikely that LLM machines will ever be capable of performing all human tasks at the skill levels of humans.