Unlike Rúmil, Fëanor considered vowels as indepedent sounds and not just “colours” of the consonants, so he devised the “full writing” (Quanta Sarmë). However he also used a more 'conservative' system which seem to have been proved far more popular. Fëanor held the idea of syllabic analysis of the words by the Sarati, and made also use of signs for vowels (instead of the full letters).
When the Noldor rebelled and came to Middle-earth, they adapted their writing for the new languages they learned. This led to the Mode of Beleriand, obviously a Quanta Sarmë modification for writing Sindarin. It is also possible that the Tengwar influenced the evolution of the Cirth, mainly in their shape and arrangement.
Tengwar are known to be used on Númenor by Men during the Second Age. The Exiles brought this Mannish usage to the Kingdom in Exile on Middle-earth, and was used to write the Common Speech. Different modes were used between Arnor and Gondor. Noteable, the Northern Mode of Arnor was a modification of the Mode of Beleriand, still used in Rivendell.