Why 160 characters
German engineer Friedhelm Hillebrand reportedly typed random sentences and questions on a typewriter and found most fitted into 160 characters. Messages travel over the network's signalling channel, which was otherwise unused, so they were cheap to run.
Why fewer with diacritics
A message without accents uses a 7-bit alphabet and fits 160 characters. Type a “č” or “ľ” and the phone switches to Unicode, dropping the limit to 70. That is why many Slovaks still write SMS without accents.
T9 and emoticons
On number keypads, T9 predictive text helped. Saving space gave rise to abbreviations and smileys. Apps such as WhatsApp have replaced SMS, but SMS is still used for verification codes (though not the most secure; see Passwords, two-factor authentication and passkeys).