This book constitutes the refereed proceedings of the 20th and 21st International Conference on Formal Grammar 2015 and 2016, collocated with the European Summer School in Logic, Language and Information in August 2015/2016. The 19 revised full papers presented together with 2 invited talks were carefully reviewed and selected from a total of 34 submissions. The focus of papers are as follows: Formal and computational phonology, morphology, syntax, semantics and pragmatics Model-theoretic and proof-theoretic methods in linguistics Logical aspects of linguistic structure Constraint-based and resource-sensitive approaches to grammar Learnability of formal grammar Integration of stochastic and symbolic models of grammar Foundational, methodological and architectural issues in grammar and linguistics Mathematical foundations of statistical approaches to linguistic analysis.