Vanilla-DataTables fires it's own events which you can listen for by utilising the .on() method:

var dataTable = new DataTable(myTable);

dataTable.on('datatable.XXXX', function(args) {
	// Do something when datatable.XXXX fires
});

Fires when the table is fully rendered and ready for use.

Fires when the .refresh() method is called.

Fires when the .update() method is called.

Fires on page change.

A single argument is available which returns the page number:

dataTable.on('datatable.page', function(page) {
    //
});

Fires when the table is sorted.

Two arguments are available when listening for this event: column which returns the column index and direction which returns the sort direction:

dataTable.on('datatable.sort', function(column, direction) {
    //
});

Fires when the perPage option is changed with the dropdown. A single argument returns the per-page value:

dataTable.on('datatable.perpage', function(perpage) {
    //
});

Fires on keyup during a search.

Two arguments are available: query which returns the query string entered and matched which returns an array of rows containing the matched string:

dataTable.on('datatable.search', function(query, matched) {
    //
});