Remove duplicates by columns A, keeping the row with the highest value in column B

This takes the last. Not the maximum though:

In [10]: df.drop_duplicates(subset='A', keep="last")
Out[10]: 
   A   B
1  1  20
3  2  40
4  3  10

You can do also something like:

In [12]: df.groupby('A', group_keys=False).apply(lambda x: x.loc[x.B.idxmax()])
Out[12]: 
   A   B
A       
1  1  20
2  2  40
3  3  10

The top answer is doing too much work and looks to be very slow for larger data sets. apply is slow and should be avoided if possible. ix is deprecated and should be avoided as well.

df.sort_values('B', ascending=False).drop_duplicates('A').sort_index()

   A   B
1  1  20
3  2  40
4  3  10

Or simply group by all the other columns and take the max of the column you need. df.groupby('A', as_index=False).max()