Most of today's web maps are using the Web Mercator projection. A major issue of Web Mercator is the distortion of area sizes far from the equator.
In 2018 Bojan Šavrič, Tom Patterson and Bernhard Jenny published their work on the Equal Earth map projection, an equal-area projection for world maps.

This site is an information collection about using the Equal Earth map projection for web mapping.
There are official EPSG codes for the following Equal Earth projection variants:
So most GIS software packages already support creating maps in Equal Earth projection.
Existing data in geographic WGS84 coordinates or in Web Mercator projection can be reprojected to Equal Earth by the map viewer.
Examples:
Other viewers:
For viewers without reprojection support, data has to be in Equal Earth projection.
A quadratic grid for Equal Earth centered on Greenwich is similar to a Web Mercator grid. Instead of Mercator grid corners at (-20'037'508, 20'037'508) and (20'037'508, -20'037'508) the grid corners of Equal Earth Greenwich are at (-17'243'959, 17'243'959) and (17'243'959, -17'243'959).

Tiles produced in Equal Earth projection on a Equal Earth Greenwich grid can be adressed with the same tile numbers by a map viewer using a Web Merctor grid. Tiles are displayed with a scale factor of 1.162. Conversions between geographic WGS84 coordinates and the map coordinate reference system give wrong results without adapted calculations. But maps can be displayed without any coordinate projection calculations.
Basic usage examples:
Examples:
Example using GDAL:
ogr2ogr ne_10m_populated_places.fgb -t_srs EPSG:8857 /vsicurl/https://github.com/nvkelso/natural-earth-vector/raw/master/geojson/ne_10m_populated_places_simple.geojson
Equal Earth projection allows the center meridian to be dynamically adjusted to the map view.

(Interactive Observable notebook)
Switching between major Equal Earth center meridians:
Equal Earth is made for world maps. For higher resolutions, Web Mercator is a better choice. Interactive maps should therefore transition from Equal Earth to Web Mercator.
Combined Equal Earth / Web Mercator vector tiles:
For feedback please open an issue or pull request on https://github.com/bbox-services/equal-earth-web-mapping