This chapter presents recent results on context-free languages, emphasizing those not covered in standard textbooks. Context-free languages were originally designed to model natural language syntax but are now widely used in programming language syntax description. Recent research focuses on algebraic treatments and open problems like the equivalence of deterministic pushdown automata and the existence of principal cones of non-generators. The chapter discusses the Hotz group, an invariant for context-free languages, and recent refinements to the proof of inherent ambiguity using generating functions. Section 2 covers iteration, including the iteration lemma, interchange lemma, and degeneracy. Section 3 explores generators and non-generators in context-free languages, with the main conjecture that the cone of non-generators is not principal. Section 4 introduces context-free groups, their word problem, and connections to Cayley graphs and ends. Key examples include Dyck languages, Lukasiewicz languages, and languages of palindromes. Ambiguity is undecidable, but techniques like iteration lemmas can prove inherent ambiguity. The chapter also discusses the relationship between context-free languages and algebraic structures, such as the Hotz group and collapsing groups. It concludes with the characterization of context-free groups and their properties. The text highlights recent developments in the theory of context-free languages, including the use of generating functions and iteration lemmas to prove non-context-freeness.This chapter presents recent results on context-free languages, emphasizing those not covered in standard textbooks. Context-free languages were originally designed to model natural language syntax but are now widely used in programming language syntax description. Recent research focuses on algebraic treatments and open problems like the equivalence of deterministic pushdown automata and the existence of principal cones of non-generators. The chapter discusses the Hotz group, an invariant for context-free languages, and recent refinements to the proof of inherent ambiguity using generating functions. Section 2 covers iteration, including the iteration lemma, interchange lemma, and degeneracy. Section 3 explores generators and non-generators in context-free languages, with the main conjecture that the cone of non-generators is not principal. Section 4 introduces context-free groups, their word problem, and connections to Cayley graphs and ends. Key examples include Dyck languages, Lukasiewicz languages, and languages of palindromes. Ambiguity is undecidable, but techniques like iteration lemmas can prove inherent ambiguity. The chapter also discusses the relationship between context-free languages and algebraic structures, such as the Hotz group and collapsing groups. It concludes with the characterization of context-free groups and their properties. The text highlights recent developments in the theory of context-free languages, including the use of generating functions and iteration lemmas to prove non-context-freeness.