Queries currently run on SQL Server

Using below Dynamic Management View (DMV) query, you can view the queries which are currently running. 

SELECT * FROM sys.dm_exec_requests

Each row represents a currently running query.

Using below query, you can view most required details of the currently running queries.

Output columns of the query:

Blocking Session ID, login  Name, Data Base Name, Status, Query Statement, Duration, Wait Type, Query Plan, Complete Percentage (If applicable eg. Backups), Estimate Completion Time (If applicable eg. Backups), Host Name

WITH cte AS (

  SELECT

              r.session_id, r.request_id, r.database_id, t.objectid, t.[text],                              r.statement_start_offset/2 AS StatementStartOffset

              , CASE WHEN r.statement_end_offset > r.statement_start_offset THEN                            r.statement_end_offset/2 ELSE LEN(t.[text]) END AS StatementEndOffset

              , p.query_plan,CAST(getdate()-r.start_time as time) Duration

              ,percent_complete, dateadd(second,estimated_completion_time/1000
              , getdate()) as estimated_completion_time,R.status,r.wait_type

  FROM sys.dm_exec_requests r

              CROSS APPLY sys.dm_exec_sql_text(r.[sql_handle]) t

              OUTER APPLY sys.dm_exec_query_plan(r.plan_handle) p

  WHERE r.[sql_handle] IS NOT NULL

), spaceUsage AS (

  SELECT

       session_id, request_id

, SUM(user_objects_alloc_page_count - user_objects_dealloc_page_count) / 128 AS UserObjMB

, SUM(internal_objects_alloc_page_count - internal_objects_dealloc_page_count) / 128 AS InternalObjMB

  FROM sys.dm_db_task_space_usage

  GROUP BY session_id, request_id

)

SELECT

       r.Session_id

       ,(SELECT DISTINCT MAX(blocking_session_id) FROM Sys.dm_os_waiting_tasks 

       WHERE blocking_session_id IS not NULL AND session_id = R.session_id) Blocking_Sid

       , REPLACE(s.login_name,'NT AUTHORITY\','') login_name
       , DB_NAME(r.database_id) AS DB_Name,R.Status

       , COALESCE('[' + OBJECT_SCHEMA_NAME(r.objectid, r.database_id) + '].[' +                     OBJECT_NAME(r.objectid, r.database_id) + ']'
       , LEFT(LTRIM(r.[text]), 128)) AS Query_Batch

       , SUBSTRING(r.[text], r.StatementStartOffset
       , r.StatementEndOffset - r.StatementStartOffset) AS Current_Statement
       ,Duration,r.Wait_Type , LEN(LEFT(r.[text], r.StatementStartOffset)) -                         LEN(REPLACE(LEFT(r.[text], r.StatementStartOffset), CHAR(10), '')) + 1 AS Line_Number

       , u.UserObjMB AS [UserObjMB*], u.InternalObjMB, r.Query_Plan

       ,Percent_Complete,   Estimated_Completion_Time,S.[Host_Name]

FROM cte r

  INNER JOIN sys.dm_exec_sessions s ON s.session_id = r.session_id

  LEFT JOIN spaceUsage u ON r.session_id = u.session_id AND r.request_id = u.request_id

And also you can use Activity Monitor to view currently running queries