Postfix TLS handshake failures with Exchange servers are often due to a combination of certificate issues (invalid, untrusted, or expired), protocol/cipher suite incompatibilities, network configuration problems, and outdated configurations. Key areas to investigate include certificate validity, TLS version support (TLS 1.2+), cipher suite matching, firewall rules, DNS and SNI settings, CRL access, MTU size, and OpenSSL restrictions. Diagnostic tools like `openssl s_client` and SSL Labs can help pinpoint the specific cause.