WhatsApp automatically makes backups every day at 3 AM and stores them in the WhatsApp folder of your Android phone. This folder is either located in your device's internal memory or external SD card. You can set the automatic backup in WhatsApp or manually use the "Back up chats" option in Whatsapp Settings,

  Whatsapp > Settings > Chats and calls > Backup up chats 

This will store a backup file(usually named msgstore.db.crypt8) in your Main storage > Whatsapp > Databases directory which includes only the text messages in an encrypted format.

For individual export of chat messages without including media, as mentioned in the Whatsapp FAQ:

To export a copy of the history of an individual chat or group, use the Email chat feature:

1. Tap and hold on the conversation or group.
2. Select Email chat.
3. Choose whether to Attach Media or not.

An email will be composed with your chat history attached as a .txt document.

Note:

• If you choose to attach media, the most recent media sent will be added as attachments.
• When sending with media, you can send up to 10,000 latest messages. Without media, you can send 40,000 messages. These constraints are due to maximum email sizes.

You can now keep this backup in your mail or download it to your phone for later use. If you want to restore the messages, read this article, How do I restore my messages? for more informatin.

WhatsApp automatically makes backups every day at 3 AM and stores them in the WhatsApp folder of your Android phone. This folder is either located in your device's internal memory or external SD card. You can set the automatic backup in WhatsApp or manually use the "Back up chats" option in Whatsapp Settings,

  Whatsapp > Settings > Chats and calls > Backup up chats 

This will store a backup file(usually named msgstore.db.crypt8) in your Main storage > Whatsapp > Databases directory which includes only the text messages in an encrypted format.

For individual export of chat messages without including media, as mentioned in the Whatsapp FAQ:

To export a copy of the history of an individual chat or group, use the Email chat feature:

1. Tap and hold on the conversation or group.
2. Select Email chat.
3. Choose whether to Attach Media or not.

An email will be composed with your chat history attached as a .txt document.

Note:

• If you choose to attach media, the most recent media sent will be added as attachments.
• When sending with media, you can send up to 10,000 latest messages. Without media, you can send 40,000 messages. These constraints are due to maximum email sizes.

You can now keep this backup in your mail or download it to your phone for later use. If you want to restore the messages, read this article, How do I restore my messages? for more information.