Finding strings which contain a given substring

Two additional methods (both faster than Select[strings, StringContainsQ["101"]]):

strings = Map[StringJoin, Tuples[{"0", "1"}, 6]];

Pick[strings, StringContainsQ["101"] @ strings]

{"000101", "001010", "001011", "001101", "010100", "010101", 
"010110", "010111", "011010", "011011", "011101", "100101", "101000", 
"101001", "101010", "101011", "101100", "101101", "101110", "101111", 
"110100", "110101", "110110", "110111", "111010", "111011", "111101"}

A slower alternative:

Pick[strings, StringMatchQ["*101*"]@strings]

same result

Two different methods:

strings = Map[StringJoin, Tuples[{"0", "1"}, 6]];
Flatten @ StringCases[
  strings,
  StartOfString ~~ ___ ~~ "101" ~~ ___ ~~ EndOfString
]
Select[strings, StringContainsQ["101"]]

The Select variant is slightly faster for large datasets.