Many assessments exist for investigating children's language. Here is a selection of commonly used assessments by speech and language therapy services in the UK:
Talking Point Check the progress of your child's language development
British Picture Vocabulary Scale (BPVS)[1] - a receptive assessment of vocabulary
Test for Reception of Grammar (TROG)[2] - understanding of language (grammar)
Preverbal Communication Schedule (PVCS) [3] - preverbal communication checklist
Clinical Evaluation of Language Fundamentals (CELF-4)[5][6] - Assesses receptive, expressive, and pragmatic language.
Clinical Evaluation of Language Fundamentals: Pre-School (CELF-P)[7] - Assesses receptive, expressive, and pragmatic language skills in Pre-School aged children.
Assessment of Comprehension and Expression 6-11 (ACE 6-11)[8] - a battery of receptive, expressive and pragmatic language tests
RAPT - picture naming and grammar/content analysis
↑Paslawski, T. (2005). "The Clinical Evaluation of Language Fundamentals, Fourth Edition (CELF-4): A Review". Canadian Journal of School Psychology20 (1–2): 129–134. doi:10.1177/0829573506295465.