The present invention includes antibodies and antigen-binding fragments thereof that specifically bind to human or cynomolgous monkey LAG3 as well as immunoglobulin chains thereof and polynucleotides encoding the same along with injection devices comprising such antibodies or fragments. Vaccines including such antibodies and fragments as well as compositions comprising the antibodies and fragments (e.g., including anti-PD1 antibodies) are included in the invention. Methods for treating or preventing cancer or infection using such compositions are also provided. In addition, methods for recombinant expression of the antibodies and fragments are part of the present invention.