Here is one cool way to solve the Number Pyramid, assuming that the puzzle is unique.

First the puzzle, with some naming convention	Then some easy filling starting with R6, then R5, then R4, then R3, then R2
Now again starting with R5, R4, R3, R2 - there are only 2 possibilities for all cells.	Now lets wait and look at Row3 first cell. If the value is 8, in Row2 first cell it can be 7 or 9. Then Row2 can't be solved uniquely.
That means the first cell in Row2 has to be 4. That gives us a good lead, and lot can be solved further.	After that there are lot of 3s and 6s and 9 in remaining cells. Keeping that in mind, the puzzle can be solved easily.For example, in the bottom row 6 can't appear anywhere other than last 2 cells.
We can also do Odd Even Marking in each cell.	Further Odd Even marking.
Now the right cell in bottom row has to be Even, because the 2nd right has to be odd.	Since R7 cell2 can't be 6, R7 first cell can't be 3. So it has to be 1 (because numbers greater than 4 can't have same number next to it in a row)

Great explanation Deb.
But I think new comers need to be a little careful while using the Uniqueness rule, it could backfire in many puzzles if used incorrectly.

I have seen people using Unique Rectangles in a Diagonal Sudoku with one of the corners of the rectangle lying on the diagonal.
Also seen puzzle creators using uniqueness while creating a puzzle, before proving that the puzzle has a unique solution.

Amit, agreed, players have to be careful while applying Uniqueness, though it provides shortcuts in many puzzles.
Also, this is not the only logical way to solve the puzzle. But i feel this is the quickest.
If other players have applied some other techniques, request them to post it here.

Thanks Deb for this great explanation. I have applied the uniqueness funda to solve this puzzle during test, but this even odd funda for new to me. Thanks again for putting this method.