Ruven

This plugin registers a custom post type for galleries and a taxonomy for categories.
Selected themes by Ruven provide templates to display galleries. 
In other themes you most likely have to add them by yourself.

Ruven Themes: Gallery

RT Gallery enables a "Gallery" post type and "Category" taxonomy.

Brecht

Use WP Ultimate Post Grid to create responsive grids for your posts, pages or any custom post type. Optionally add an isotope filter for any taxonomy associated with those posts.
<blockquote>
See this plugin in action! 
 Check out <a href="https://bootstrapped.ventures/wp-ultimate-post-grid/" rel="nofollow ugc">demos of our grids</a> and all of the <a href="https://help.bootstrapped.ventures/collection/7-wp-ultimate-post-grid" rel="nofollow ugc">plugin documentation</a> to learn more.
</blockquote>
An overview of the WP Ultimate Post Grid features:
<ul>
<li>Live Preview while building your grid</li>
<li>Use posts, pages or custom post types as the source</li>
<li>Grids are responsive and will look good on any device</li>
<li>Ability to set order by options</li>
<li>Link to the actual post or featured image</li>
<li>Define custom links for posts</li>
<li>Define custom images for posts</li>
<li>Add an isotope filter for any taxonomy or custom field</li>
<li>Deeplinking directly to a filtered grid</li>
<li>Grids and filters can be added anywhere with their own shortcode</li>
<li>Multiple templates for your grids</li>
<li>Extensive Template Editor to create any grid you want</li>
<li>Possibility to use pagination</li>
<li>Compatible with both Classic Editor and Gutenberg Block Editor</li>
<li>Fully integrated with our WP Recipe Maker plugin for a recipe grid</li>
</ul>
We also have a <a href="https://bootstrapped.ventures/wp-ultimate-post-grid/" rel="nofollow ugc">WP Ultimate Post Grid Premium version</a> which offers the following features:
<ul>
<li>Limit your posts by any taxonomy, author, date or post ID</li>
<li>Use a plain text filter for your grid</li>
<li>Have dropdown filters for any taxonomy</li>
<li>Use a checkbox filter for any taxonomy</li>
<li>Allow for multiselect in the filters</li>
<li>Show the post count for the filter terms</li>
<li>Create a grid of your categories or tags</li>
<li>A Load More button for pagination</li>
<li>Load on filter pagination</li>
<li>Infinite scroll pagination</li>
<li>Easily clone your grids</li>
<li>Order grid by custom field</li>
<li>Dynamically filter grids in the shortcode</li>
</ul>
This plugin is under active development. Any feature requests are welcome!

WP Ultimate Post Grid

Easily create filterable responsive grids for your posts, pages or custom post types

Ruven Themes: Gallery vs WP Ultimate Post Grid