More robust built-in filtering - Starts with, ends with, regular expressions, match case ... list of values and let user choose
Got examples from other products or from the web we should reference?
Devexpress team made an excellent work here: Devexpress DataGrid Demo
Great example. Thx @akhedrane
Kendo ui has a great example of this and several other features mentioned. They're be some design transition to material but much would still apply http://www.telerik.com/kendo-ui/grid

This screen capture shows multi-column and global filtering as currently implemented in Studio Lite using the PrimeNg data table.

The advantage to this approach is that the filter values remain visible as long as the filters are not hidden. From a UX perspective, being able to see all the filter values at a glance is very useful.
Thinking about the close relationship between filtering and searching, I think that combining the two into a unified interface would be ideal.
If we combine the two, filtering becomes just a toggle option of search (show only matching rows).
For example, reworking the current filter implementation shown above:

That's a great example thanks
Support for different match modes is also important (e.g. contains, startsWith, endsWith, equals, regex).
This could be added as a drop down selector.

Again the UX is enhanced by showing the match mode in a concise way (<, >, <>, =, *)
The event emitted for search/filter could be something like
{
filter: true,
globalSearch: {value: "a[bcd]e", matchMode: "regex"},
columnSearch: [
{name: "column1", value: "44", matchMode: "contains"},
{name: "column2", value: "ab", matchMode: "startsWith"},
{name: "column3", value: "55", matchMode: "equals"}
]
}
Hi, will this be part of release 2.0.0?
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Devexpress team made an excellent work here: Devexpress DataGrid Demo