In fact this is incorrect. They MAY be CRUD-like or MAY be something else. The rule is: each resource MUST have a set of predefined operation. But not necessary CRUD. Even not necessary GET-POST-PUT-DELETE should be used. In fact did you know that HTTP/1.1 defines 8 HTTP Verbs: HEAD, GET, POST, PUT, DELETE, OPTIONS, TRACE and CONNECT? And in addition you may define your own HTTP Verbs that will behave as you wish? For example WebDAV defines the following verbs in addition to the standard ones: PROPFIND, PROPPATCH, MKCOL, COPY, MOVE, LOCK, UNLOCK.
So now, when you know that you may not stick to the standard HTTP verbs, I still advocate you to do so. Why? It's relatively clear what action these methods will do with the resource. It's may be less clear what action your own verb will do.
So let's consider that 90% of RESTful APIs will use only the standard HTTP verbs. What's important to pay attention to? The most important rule is to use the HTTP verbs correctly. The most common example of an incorrect use of the GET verb can be taken from HTML forms: in HTML both GET and POST can be used to submit data to a server from a form. But actually GET is a safe method, it means that it SHOULD NOT have the significance of taking an action other than retrieval.
So remember, Rule 1: HEAD and GET are safe methods.
Now about the Idempotent Methods. Methods are idempotent if the side-effects of N > 0 identical requests is the same as for a single request. The idempotent methods are GET, HEAD, PUT and DELETE.
Some examples what does it mean:
1. PUT can be used to create a resource. Yes, I know that the best practice say that it is POST, who creates resources and in a second I'll explain why. So let's say PUT creates a resource, but if a request is duplicated for some reason, the second request must not create a new resource and return exactly the same response as the first request. It's important to understand that various HTTP intermediaries know that PUT is idempotent and for example they may apply some caching, etc. So actually POST is much safer, especially for creating resources. But pay attention: POST may be safely used also for updates and even fetching the resource! Nobody said it is only for creation.
2. When DELETE-ing the resource, pay attention that the second DELETE request should return the same response. So if a first response returns "200 OK", the second (third, fourth, etc) DELETE requests to the same resource also should return "200 OK". Pay attention that once the resource was deleted, the GET request to this resource should return "404 NOT FOUND", but DELETE should continue returning "200 OK".
So Rule 2 will be: use idempotent methods correctly. If you cannot ensure that you use them correctly, use other methods and POST can be a good choice.
Now a little about the methods that you are unlikely to implement yourself. The behavior of the HEAD, TRACE, CONNECT and OPTIONS is well defined and they are usually implemented by the infrastructure (CONNECT and TRACE by the web servers, HEAD and OPTIONS by the frameworks, like Servlets or JAX-RS). If, for some reason, you decide to implement one of these methods, make sure your do it correctly.
Summary1. Don't try to map CRUD to HTTP verbs. There is no need to do it.
2. Create new HTTP verbs, if needed.
3. Use existing HTTP verbs correctly, pay special attention to the safe methods (HEAD and GET) and to the idempotent methods (HEAD, GET, PUT and DELETE).
4. If you are now sure which HTTP verb to choose, use POST.