Do some sentences not start with a capital?

You're right! There are a few cases where sentences don't start with a capital letter:

* Sentence fragments: These are incomplete sentences that lack a subject or verb. For example, "Running down the street."

* Quoted material within a sentence: If a quotation starts within a sentence, it doesn't need a capital unless it's a complete sentence on its own. Example: "He said, 'I'm going to the store.'"

* Titles and headings: Often, only the first word of a title or heading is capitalized, even if it's a complete sentence.

Let me know if you'd like more examples!