I know object dtype columns makes the data hard to convert with pandas functions. When I receive data like this, the first thing that came to mind was to "flatten" or unnest the columns.

I am using pandas and Python functions for this type of question. If you are worried about the speed of the above solutions, check out user3483203's answer, since it's using numpy and most of the time numpy is faster. I recommend Cython or numba if speed matters.

Method 0 [pandas >= 0.25] Starting from pandas 0.25, if you only need to explode one column, you can use the pandas.DataFrame.explode function:

df.explode('B')

       A  B
    0  1  1
    1  1  2
    0  2  1
    1  2  2

Given a dataframe with an empty list or a NaN in the column. An empty list will not cause an issue, but a NaN will need to be filled with a list

df = pd.DataFrame({'A': [1, 2, 3, 4],'B': [[1, 2], [1, 2], [], np.nan]})
df.B = df.B.fillna({i: [] for i in df.index})  # replace NaN with []
df.explode('B')

   A    B
0  1    1
0  1    2
1  2    1
1  2    2
2  3  NaN
3  4  NaN

Method 1 apply + pd.Series (easy to understand but in terms of performance not recommended . )

df.set_index('A').B.apply(pd.Series).stack().reset_index(level=0).rename(columns={0:'B'})
Out[463]:
   A  B
0  1  1
1  1  2
0  2  1
1  2  2

Method 2 Using repeat with DataFrame constructor , re-create your dataframe (good at performance, not good at multiple columns )

df=pd.DataFrame({'A':df.A.repeat(df.B.str.len()),'B':np.concatenate(df.B.values)})
df
Out[465]:
   A  B
0  1  1
0  1  2
1  2  1
1  2  2

Method 2.1 for example besides A we have A.1 .....A.n. If we still use the method(Method 2) above it is hard for us to re-create the columns one by one .

Solution : join or merge with the index after 'unnest' the single columns

s=pd.DataFrame({'B':np.concatenate(df.B.values)},index=df.index.repeat(df.B.str.len()))
s.join(df.drop('B',1),how='left')
Out[477]:
   B  A
0  1  1
0  2  1
1  1  2
1  2  2

If you need the column order exactly the same as before, add reindex at the end.

s.join(df.drop('B',1),how='left').reindex(columns=df.columns)

Method 3 recreate the list

pd.DataFrame([[x] + [z] for x, y in df.values for z in y],columns=df.columns)
Out[488]:
   A  B
0  1  1
1  1  2
2  2  1
3  2  2

If more than two columns, use

s=pd.DataFrame([[x] + [z] for x, y in zip(df.index,df.B) for z in y])
s.merge(df,left_on=0,right_index=True)
Out[491]:
   0  1  A       B
0  0  1  1  [1, 2]
1  0  2  1  [1, 2]
2  1  1  2  [1, 2]
3  1  2  2  [1, 2]

Method 4 using reindex or loc

df.reindex(df.index.repeat(df.B.str.len())).assign(B=np.concatenate(df.B.values))
Out[554]:
   A  B
0  1  1
0  1  2
1  2  1
1  2  2

#df.loc[df.index.repeat(df.B.str.len())].assign(B=np.concatenate(df.B.values))

Method 5 when the list only contains unique values:

df=pd.DataFrame({'A':[1,2],'B':[[1,2],[3,4]]})
from collections import ChainMap
d = dict(ChainMap(*map(dict.fromkeys, df['B'], df['A'])))
pd.DataFrame(list(d.items()),columns=df.columns[::-1])
Out[574]:
   B  A
0  1  1
1  2  1
2  3  2
3  4  2

Method 6 using numpy for high performance:

newvalues=np.dstack((np.repeat(df.A.values,list(map(len,df.B.values))),np.concatenate(df.B.values)))
pd.DataFrame(data=newvalues[0],columns=df.columns)
   A  B
0  1  1
1  1  2
2  2  1
3  2  2

Method 7 using base function itertools cycle and chain: Pure python solution just for fun

from itertools import cycle,chain
l=df.values.tolist()
l1=[list(zip([x[0]], cycle(x[1])) if len([x[0]]) > len(x[1]) else list(zip(cycle([x[0]]), x[1]))) for x in l]
pd.DataFrame(list(chain.from_iterable(l1)),columns=df.columns)
   A  B
0  1  1
1  1  2
2  2  1
3  2  2

Generalizing to multiple columns

df=pd.DataFrame({'A':[1,2],'B':[[1,2],[3,4]],'C':[[1,2],[3,4]]})
df
Out[592]:
   A       B       C
0  1  [1, 2]  [1, 2]
1  2  [3, 4]  [3, 4]

Self-def function:

def unnesting(df, explode):
    idx = df.index.repeat(df[explode[0]].str.len())
    df1 = pd.concat([
        pd.DataFrame({x: np.concatenate(df[x].values)}) for x in explode], axis=1)
    df1.index = idx

    return df1.join(df.drop(explode, 1), how='left')


unnesting(df,['B','C'])
Out[609]:
   B  C  A
0  1  1  1
0  2  2  1
1  3  3  2
1  4  4  2

Column-wise Unnesting

All above method is talking about the vertical unnesting and explode , If you do need expend the list horizontal, Check with pd.DataFrame constructor

df.join(pd.DataFrame(df.B.tolist(),index=df.index).add_prefix('B_'))
Out[33]:
   A       B       C  B_0  B_1
0  1  [1, 2]  [1, 2]    1    2
1  2  [3, 4]  [3, 4]    3    4

Updated function

def unnesting(df, explode, axis):
    if axis==1:
        idx = df.index.repeat(df[explode[0]].str.len())
        df1 = pd.concat([
            pd.DataFrame({x: np.concatenate(df[x].values)}) for x in explode], axis=1)
        df1.index = idx

        return df1.join(df.drop(explode, 1), how='left')
    else :
        df1 = pd.concat([
                         pd.DataFrame(df[x].tolist(), index=df.index).add_prefix(x) for x in explode], axis=1)
        return df1.join(df.drop(explode, 1), how='left')

Test Output

unnesting(df, ['B','C'], axis=0)
Out[36]:
   B0  B1  C0  C1  A
0   1   2   1   2  1
1   3   4   3   4  2

Update 2021-02-17 with original explode function

def unnesting(df, explode, axis):
    if axis==1:
        df1 = pd.concat([df[x].explode() for x in explode], axis=1)
        return df1.join(df.drop(explode, 1), how='left')
    else :
        df1 = pd.concat([
                         pd.DataFrame(df[x].tolist(), index=df.index).add_prefix(x) for x in explode], axis=1)
        return df1.join(df.drop(explode, 1), how='left')

Option 1

If all of the sublists in the other column are the same length, numpy can be an efficient option here:

vals = np.array(df.B.values.tolist())    
a = np.repeat(df.A, vals.shape[1])

pd.DataFrame(np.column_stack((a, vals.ravel())), columns=df.columns)

   A  B
0  1  1
1  1  2
2  2  1
3  2  2

Option 2

If the sublists have different length, you need an additional step:

vals = df.B.values.tolist()
rs = [len(r) for r in vals]    
a = np.repeat(df.A, rs)

pd.DataFrame(np.column_stack((a, np.concatenate(vals))), columns=df.columns)

   A  B
0  1  1
1  1  2
2  2  1
3  2  2

Option 3

I took a shot at generalizing this to work to flatten N columns and tile M columns, I'll work later on making it more efficient:

df = pd.DataFrame({'A': [1,2,3], 'B': [[1,2], [1,2,3], [1]],
                   'C': [[1,2,3], [1,2], [1,2]], 'D': ['A', 'B', 'C']})

   A          B          C  D
0  1     [1, 2]  [1, 2, 3]  A
1  2  [1, 2, 3]     [1, 2]  B
2  3        [1]     [1, 2]  C

def unnest(df, tile, explode):
    vals = df[explode].sum(1)
    rs = [len(r) for r in vals]
    a = np.repeat(df[tile].values, rs, axis=0)
    b = np.concatenate(vals.values)
    d = np.column_stack((a, b))
    return pd.DataFrame(d, columns = tile +  ['_'.join(explode)])

unnest(df, ['A', 'D'], ['B', 'C'])

    A  D B_C
0   1  A   1
1   1  A   2
2   1  A   1
3   1  A   2
4   1  A   3
5   2  B   1
6   2  B   2
7   2  B   3
8   2  B   1
9   2  B   2
10  3  C   1
11  3  C   1
12  3  C   2

Functions

def wen1(df):
    return df.set_index('A').B.apply(pd.Series).stack().reset_index(level=0).rename(columns={0: 'B'})

def wen2(df):
    return pd.DataFrame({'A':df.A.repeat(df.B.str.len()),'B':np.concatenate(df.B.values)})

def wen3(df):
    s = pd.DataFrame({'B': np.concatenate(df.B.values)}, index=df.index.repeat(df.B.str.len()))
    return s.join(df.drop('B', 1), how='left')

def wen4(df):
    return pd.DataFrame([[x] + [z] for x, y in df.values for z in y],columns=df.columns)

def chris1(df):
    vals = np.array(df.B.values.tolist())
    a = np.repeat(df.A, vals.shape[1])
    return pd.DataFrame(np.column_stack((a, vals.ravel())), columns=df.columns)

def chris2(df):
    vals = df.B.values.tolist()
    rs = [len(r) for r in vals]
    a = np.repeat(df.A.values, rs)
    return pd.DataFrame(np.column_stack((a, np.concatenate(vals))), columns=df.columns)

Timings

import pandas as pd
import matplotlib.pyplot as plt
import numpy as np
from timeit import timeit

res = pd.DataFrame(
       index=['wen1', 'wen2', 'wen3', 'wen4', 'chris1', 'chris2'],
       columns=[10, 50, 100, 500, 1000, 5000, 10000],
       dtype=float
)

for f in res.index:
    for c in res.columns:
        df = pd.DataFrame({'A': [1, 2], 'B': [[1, 2], [1, 2]]})
        df = pd.concat([df]*c)
        stmt = '{}(df)'.format(f)
        setp = 'from __main__ import df, {}'.format(f)
        res.at[f, c] = timeit(stmt, setp, number=50)

ax = res.div(res.min()).T.plot(loglog=True)
ax.set_xlabel("N")
ax.set_ylabel("time (relative)")

Performance

Exploding a list-like column has been simplified significantly in pandas 0.25 with the addition of the explode() method:

df = pd.DataFrame({'A': [1, 2], 'B': [[1, 2], [1, 2]]})
df.explode('B')

Out:

   A  B
0  1  1
0  1  2
1  2  1
1  2  2