The structure of the Standard Model (SM) of particle physics points toward grand unified
theories (GUTs) where strong and electroweak interactions are unified
in a non-Abelian GUT group. The spontaneous breaking of the GUT
symmetry to the SM symmetry, together with cosmic inflation,
generically leads to metastable topological defects, the most
prominent example being cosmic strings. The gravitational-wave
background (GWB) produced by a cosmic string network is one of the
candidates for an explanation of the GWB recently observed by pulsar
timing array (PTA) experiments. We review some properties of the
predicted GWB with emphasis on potential implications for GUT model
building. The most striking prediction is a GWB in the
LIGO-Virgo-KAGRA band that could be discovered in the near future.