Must blockquotes contain paragraphs or must paragraphs contain blockquotes?

Question

In HTML5, is it correct to put blockquotes inside paragraphs or is the opposite the right way? I mean, logic tells that a blockquote may be citing multiple paragraps, doesn't it?

But doesn't blockquotes need to contain q elements? Could someone explain me the right structure?

EDIT: To add some info. I got this doubt because when trying to implement quotation marks with CSS, they don't appear on blockquote but they do on q elements. What is the right way to do this?

blockquote, q {
  quotes: "\201C""\201D""\2018""\2019";
  font-style: italic;
}

<blockquote>
  <p>Hello!</p>
  <p>Say something!</p>
</blockquote>
<p>He told me <q>Say something!</q>
</p>

Answer 1

According to the specifications provided by the W3 group the blockquote is a block level semantic that should contain the entire quote, which can be made up of multiple paragraphs. Because the blockquote itself contains one or more paragraphs(or other elements), it doesn't make much sense to put it inside a paragraph. An example, provided by the W3G:

<blockquote>
    <p>My favorite book is <cite class="from-source">At Swim-Two-Birds</cite></p>
    <footer>- <cite>Mike[tm]Smith</cite></footer>
</blockquote>

As you can see, the example blockquote contains text that's inside of p elements, but not inside of q elements.

The q element is a text level semantic and it should be used to indicate that part of the text is a quotation. Because the blockquote already indicates quotation, marking the text inside with q-elements is not necessary. An example, taken from the W3G specification:

<p>The man said <q>Things that are impossible just take longer</q>. I disagreed with him.</p>

Long story short: if you use a blockquote element, put other elements (such as p elements) inside of it, but it's not necessary to use q elements inside a blockquote.