How can I make blockquotes in LaTeX, like Markdown

Question

In Markdown, use a pair of ``` to block quotes,

How can I achieve it in LaTeX?

I use the packet csquotes and encounter two questions:

• how to remove double quotes
• how to add background color

Answer 1

For the color part of the problem, I used a tcolorbox approach as given in the answer to this question: Change background color for text block

For the markdown parsing one can borrow and adapt from my answer at Use Markdown-style formatting for bold and italic.

Here I interpret triple backticks as delimiters for a myquote environment, using the macro \triplequote. Not knowing from your question how to interpret single and double backticks, I merely show how they are parsed, using placeholders defined in the macros \singlequote and \doublequote.

The macros \quoteON and \quoteOFF are used to enable and disable the active parsing.

\documentclass{article}
\usepackage[most]{tcolorbox}
\definecolor{block-gray}{gray}{0.85}
\newtcolorbox{myquote}{colback=block-gray,grow to right by=-10mm,grow to left by=-10mm,
boxrule=0pt,boxsep=0pt,breakable}
\makeatletter
\def\quoteparse{\@ifnextchar`{\quotex}{\singlequote}}
\def\quotex#1{\@ifnextchar`{\triplequote\@gobble}{\doublequote}}
\makeatother
\def\singlequote#1`{[StartQ]#1[EndQ]\quoteON}
\def\doublequote#1``{[StartQQ]#1[EndQQ]\quoteON}
\long\def\triplequote#1```{\begin{myquote}\parskip 1ex#1\end{myquote}\quoteON}
\def\quoteON{\catcode``=\active}
\def\quoteOFF{\catcode``=12}
\quoteON
\def`{\quoteOFF \quoteparse}
\quoteOFF
\begin{document}
\quoteON
This is a `test of single quoted` material 
and this is a ``test of double quoted material``, and this
is the test of a ```triple quoted material. We will make it long
enough to test line wrapping and we will even\\
add a manual linebreak.

Even a new paragraph.```  Resuming normal text.

\quoteOFF
Here should be triple backticks ```xxx```
\end{document}

Once it is known how single-quoted and double-quoted material should behave, those macros can be adjusted to implement it.