[Dim Period] dimension values:
For this demo, I have a dimension called [Dim Period] in my SSAS cube which looks like:

All values
So here’s how you could diplays all values (children) of a certain dimension:


Filtered by NOW()/FORMAT
([Dim Period].[Id].&[200701] : StrToMember("[Dim Period].[Id].&[" + Format(Now(), "yyyyMM") + "]")


Filtered by HAVING
HAVING NOT ISEMPTY([Measures].[--Value--])


Code
Here’s the MDX script I used:
--All members in the [Dim Period] dimension:
WITH
MEMBER [Measures].[ParameterCaption] AS [Dim Period].[Period Description].CURRENTMEMBER.MEMBER_CAPTION
MEMBER [Measures].[ParameterValue] AS [Dim Period].[Id].CURRENTMEMBER.UNIQUENAME
SELECT
{
[Measures].[ParameterCaption]
,[Measures].[ParameterValue]
} ON COLUMNS,
ORDER([Dim Period].[Id].CHILDREN,[Dim Period].[Id].CurrentMember.Member_Name,DESC) ON ROWS
FROM [CUBE]
--Filtered based on the current date:
WITH
MEMBER [Measures].[ParameterCaption] AS [Dim Period].[Period Description].CURRENTMEMBER.MEMBER_CAPTION
MEMBER [Measures].[ParameterValue] AS [Dim Period].[Id].CURRENTMEMBER.UNIQUENAME
SELECT
{
[Measures].[ParameterCaption]
,[Measures].[ParameterValue]
} ON COLUMNS,
ORDER([Dim Period].[Id].CHILDREN,[Dim Period].[Id].CurrentMember.Member_Name,DESC) ON ROWS
FROM
(
SELECT
--Here's a trick that will work on date/time values:
([Dim Period].[Id].&[200701] : StrToMember("[Dim Period].[Id].&[" + Format(Now(), "yyyyMM") + "]")
) ON COLUMNS
FROM [CUBE]
)
--But for other non time related dimensional members, you need to a different method:
WITH
MEMBER [Measures].[ParameterCaption] AS [Dim Period].[Period Description].CURRENTMEMBER.MEMBER_CAPTION
MEMBER [Measures].[ParameterValue] AS [Dim Period].[Id].CURRENTMEMBER.UNIQUENAME
SELECT
{
[Measures].[ParameterCaption]
,[Measures].[ParameterValue]
} ON COLUMNS,
ORDER([Dim Period].[Id].CHILDREN,[Dim Period].[Id].CurrentMember.Member_Name,DESC)
HAVING NOT ISEMPTY([Measures].[BS Balance])
ON ROWS
FROM [CUBE]