  Many automatic sequences, such as the Thue-Morse sequence or the
Rudin-Shapiro sequence, have some desirable features of pseudorandomness such
as a large linear complexity and a small well-distribution measure. However,
they also have some disastrous properties in view of certain applications. For
example, the majority of possible binary patterns never appears in automatic
sequences and their correlation measure of order 2 is extremely large.
  Certain subsequences, such as automatic sequences along squares, may keep the
good properties of the original sequence but avoid the bad ones.
  In this survey we investigate properties of pseudorandomness and
non-randomness of automatic sequences and their subsequences and present
results on their behaviour under several measures of pseudorandomness including
linear complexity, correlation measure of order $k$, expansion complexity and
normality. We also mention some analogs for finite fields.
