Monitoring the progress of a calculation over a list

Here's a solution using ResourceFunction["MonitorProgress"]:

fun[x_] := (Pause@1(*some long computation *);x^2)

ResourceFunction["MonitorProgress"][fun /@ Range@5]
(* {1, 4, 9, 16, 25} *)

You can add Print[], PrintTemporary[] or Echo[] to your function definition.

ClearAll[fun] ;
fun[x_] := (Pause[1]; Echo[x] ; x)
list = Range[10] ;
Map[fun,list]

ClearAll[fun] ;
fun[x_] := (Pause[1]; PrintTemporary[x] ; x)
list = Range[10] ;
Map[fun,list]

Also Dynamic[] and Monitor[] can be used:

ClearAll[fun] ;
fun[x_] := (Pause[1]; Dynamic[count] ; count++ ; x)
count = 1 ;
list = Range[10] ;
Monitor[Map[fun,list],ProgressIndicator[count,{1, Length[list]}]]