From &str

• &str -> String has many equally valid methods: String::from(st), st.to_string(), st.to_owned().
  • But I suggest you stick with one of them within a single project. The major advantage of String::from is that you can use it as an argument to a map method. So instead of x.map(|s| String::from(s)) you can often use x.map(String::from).
• &str -> &[u8] is done by st.as_bytes()
• &str -> Vec<u8> is a combination of &str -> &[u8] -> Vec<u8>, i.e. st.as_bytes().to_vec() or st.as_bytes().to_owned()

From String

• String -> &str should just be &s where coercion is available or s.as_str() where it is not.
• String -> &[u8] is the same as &str -> &[u8]: s.as_bytes()
• String -> Vec<u8> has a custom method: s.into_bytes()

From &[u8]

• &[u8] -> Vec<u8> is done by u.to_owned() or u.to_vec(). They do the same thing, but to_vec has the slight advantage of being unambiguous about the type it returns.
• &[u8] -> &str doesn’t actually exist, that would be &[u8] -> Result<&str, Error>, provided via str::from_utf8(u)
  • str::from_utf8(u).unwrap() works, but you should prefer better error handling (see Error handling – The Result type).
• &[u8] -> String is the combination of &[u8] -> Result<&str, Error> -> Result<String, Error>
  • String::from_utf8(u).unwrap() works, but prefer better error handling (see Error handling – The Result type and also Result::map.

From Vec<u8>

• Vec<u8> -> &[u8] should be just &v where coercion is available, or as_slice where it’s not.
• Vec<u8> -> &str is the same as Vec<u8> -> &[u8] -> Result<&str, Error> i.e. str::from_utf8(&v)
  • str::from_utf8(&v).unwrap() works, but prefer better error handling (see Error handling – The Result type)
• Vec<u8> -> String doesn’t actually exist, that would be Vec<u8> -> Result<String, Error> via String::from_utf8(v)
  • String::from_utf8(v).unwrap() works, but prefer better error handling (see Error handling – The Result type).

Coercion is available whenever the target is not generic but explicitly typed as &str or &[u8], respectively. The Rustonomicon has a chapter on coercions with more details about coercion sites.

tl;dr

&str    -> String  | String::from(s) or s.to_string() or s.to_owned()
&str    -> &[u8]   | s.as_bytes()
&str    -> Vec<u8> | s.as_bytes().to_vec() or s.as_bytes().to_owned()
String  -> &str    | &s if possible* else s.as_str()
String  -> &[u8]   | s.as_bytes()
String  -> Vec<u8> | s.into_bytes()
&[u8]   -> &str    | s.to_vec() or s.to_owned()
&[u8]   -> String  | std::str::from_utf8(s).unwrap(), but don't**
&[u8]   -> Vec<u8> | String::from_utf8(s).unwrap(), but don't**
Vec<u8> -> &str    | &s if possible* else s.as_slice()
Vec<u8> -> String  | std::str::from_utf8(&s).unwrap(), but don't**
Vec<u8> -> &[u8]   | String::from_utf8(s).unwrap(), but don't**

* target should have explicit type (i.e., checker can't infer that)

** handle the error properly instead