  This letter proposes successive cancellation list (SCL) decoding of product
codes with Reed--Muller (RM) component codes. SCL decoding relies on a product
code description based on the $2\times 2$ Hadamard kernel, which enables
interpreting the code as an RM subcode. The focus is on a class of product
codes considered in wireless communication systems, based on single
parity-check and extended Hamming component codes. For short product codes, it
is shown that SCL decoding with a moderate list size performs as well as (and,
sometimes, outperforms) belief propagation (BP) decoding. Furthermore, by
concatenating a short product code with a high-rate outer code, SCL decoding
outperforms BP decoding by up to $1.4$ dB.
