What are the language tests one can take to apply under the Express Entry program?

Canadian immigration authorities accept the following tests for Express Entry:

For English

CELPIP: Canadian English Language Proficiency Index Program – CELPIP-General

IELTS: International English Language Testing System – General Training

PTE Core: Pearson Test of English. You must take the PTE Core option

For French

TEF Canada: Test d’évaluation de français

TCF Canada : Test de connaissance du français