Instead of using traditional HTML table elements, it is also possible to convert a structure of non-table elements into a table using ARIA. This is an experiment, and we explicitly do not recommend using this on productive websites. So please, kids, do not try this at home!
A table of divs
As we have seen, it is possible to re-apply semantics to an element that has somehow lost its inherent semantics. This is done using ARIA (if you haven't done this yet, go back and read Responsive tables).
We can try to follow this approach "ad absurdum" by trying to add all needed semantics using ARIA alone.
So the following example is an experiment with a purely demonstrative purpose. It contains an HTML structure that is made of pure <div> elements (so nothing like <table>, <tr>, <td>, or similar was used). Thanks to adding an appropriate role attribute to each element, it is conveyed to screen readers like a table.
<pid="caption">My Hobbies</p><divaria-describedby="caption"class="table"role="table"><divclass="tr"role="row"><divclass="th"role="columnheader">Name</div><divclass="th"role="columnheader">Description</div><divclass="th"role="columnheader">Additional Resources</div></div><divclass="tr"role="row"><divclass="th"role="rowheader">Playing Soccer</div><divclass="td"role="cell">
Soccer is a team sport played between two teams of eleven players with a
spherical ball.
</div><divclass="td"role="cell"><ahref="https://en.wikipedia.org/wiki/Association_football">Wikipedia</a></div></div><divclass="tr"role="row"><divclass="th"role="rowheader">Dancing</div><divclass="td"role="cell">
Dance is a performing art form consisting of purposefully selected
sequences of human movement.
</div><divclass="td"role="cell"><ahref="https://en.wikipedia.org/wiki/Dance">Wikipedia</a></div></div><divclass="tr"role="row"><divclass="th"role="rowheader">Gardening</div><divclass="td"role="cell">
Gardening is the practice of growing and cultivating plants as part of
horticulture.
</div><divclass="td"role="cell"><ahref="https://en.wikipedia.org/wiki/Gardening">Wikipedia</a></div></div></div>
As all roles can be set explicitly using ARIA, we are not restricted anymore styling the table in any traditional way. For example, instead of using display: table, display: table-row, and display: table-cell, etc., we can now style a table as flexbox:
<pid="caption">My Hobbies</p><divaria-describedby="caption"class="table"role="table"><divclass="tr"role="row"><divclass="th"role="columnheader">Name</div><divclass="th"role="columnheader">Description</div><divclass="th"role="columnheader">Additional Resources</div></div><divclass="tr"role="row"><divclass="th"role="rowheader">Playing Soccer</div><divclass="td"role="cell">
Soccer is a team sport played between two teams of eleven players with a
spherical ball.
</div><divclass="td"role="cell"><ahref="https://en.wikipedia.org/wiki/Association_football">Wikipedia</a></div></div><divclass="tr"role="row"><divclass="th"role="rowheader">Dancing</div><divclass="td"role="cell">
Dance is a performing art form consisting of purposefully selected
sequences of human movement.
</div><divclass="td"role="cell"><ahref="https://en.wikipedia.org/wiki/Dance">Wikipedia</a></div></div><divclass="tr"role="row"><divclass="th"role="rowheader">Gardening</div><divclass="td"role="cell">
Gardening is the practice of growing and cultivating plants as part of
horticulture.
</div><divclass="td"role="cell"><ahref="https://en.wikipedia.org/wiki/Gardening">Wikipedia</a></div></div></div>
When tinkering up a table using random HTML elements and ARIA roles, it is very important that the used structure of elements (and roles) resembles a valid HTML table.
A slightly invalid structure
The following example adds another <div class="favorites"> container around the second and third hobby's <tr> elements so we can style those individually. This breaks the table for some screen readers: for example, NVDA announces it as "table with 2 rows and 3 columns" (instead of 4 rows), and for the second and third hobby, table navigation does not work anymore.
<pid="caption">My Hobbies</p><divaria-describedby="caption"class="table"role="table"><divclass="tr"role="row"><divclass="th"role="columnheader">Name</div><divclass="th"role="columnheader">Description</div><divclass="th"role="columnheader">Additional Resources</div></div><divclass="tr"role="row"><divclass="th"role="rowheader">Playing Soccer</div><divclass="td"role="cell">
Soccer is a team sport played between two teams of eleven players with a
spherical ball.
</div><divclass="td"role="cell"><ahref="https://en.wikipedia.org/wiki/Association_football">Wikipedia</a></div></div><divclass="favourites"><divclass="tr"role="row"><divclass="th"role="rowheader">Dancing</div><divclass="td"role="cell">
Dance is a performing art form consisting of purposefully selected
sequences of human movement.
</div><divclass="td"role="cell"><ahref="https://en.wikipedia.org/wiki/Dance">Wikipedia</a></div></div><divclass="tr"role="row"><divclass="th"role="rowheader">Gardening</div><divclass="td"role="cell">
Gardening is the practice of growing and cultivating plants as part of
horticulture.
</div><divclass="td"role="cell"><ahref="https://en.wikipedia.org/wiki/Gardening">Wikipedia</a></div></div></div></div>
This should not be too much surprising: in standard HTML, adding a container around <tr> elements is not valid, either. And although the above example is still working in some screen readers, the following always holds true: the messier the HTML code is, the more problems will occur.
Making it valid again
The good news: by adding role="presentation" to this additional container, we remove its semantical meaning, and the table is working again (also in NVDA).
<pid="caption">My Hobbies</p><divaria-describedby="caption"class="table"role="table"><divclass="tr"role="row"><divclass="th"role="columnheader">Name</div><divclass="th"role="columnheader">Description</div><divclass="th"role="columnheader">Additional Resources</div></div><divclass="tr"role="row"><divclass="th"role="rowheader">Playing Soccer</div><divclass="td"role="cell">
Soccer is a team sport played between two teams of eleven players with a
spherical ball.
</div><divclass="td"role="cell"><ahref="https://en.wikipedia.org/wiki/Association_football">Wikipedia</a></div></div><divclass="favourites"role="presentation"><divclass="tr"role="row"><divclass="th"role="rowheader">Dancing</div><divclass="td"role="cell">
Dance is a performing art form consisting of purposefully selected
sequences of human movement.
</div><divclass="td"role="cell"><ahref="https://en.wikipedia.org/wiki/Dance">Wikipedia</a></div></div><divclass="tr"role="row"><divclass="th"role="rowheader">Gardening</div><divclass="td"role="cell">
Gardening is the practice of growing and cultivating plants as part of
horticulture.
</div><divclass="td"role="cell"><ahref="https://en.wikipedia.org/wiki/Gardening">Wikipedia</a></div></div></div></div>
While pure ARIA tables seem to work pretty well in most modern screen readers, we highly discourage using them in productive websites.
Generally speaking, the above example is a case of one of ARIA's typical mis-usages, namely fixing broken semantics (if you haven't done this yet, go back and read Bad ARIA practices).
The use of real, traditional table structures makes it much easier to spot table-like data directly in the DOM. Also, they are fully backwards compatible, while ARIA requires pretty advanced browsers and screen readers.