Used to introduce a new topic or to add to what was being discussed.

वैसे

English Usage: By the way, did you finish your homework?

Hindi Usage: वैसे, क्या तुमने अपना होमवर्क पूरा किया?

According to what people say or according to the way the story is told

जैसा कि कहानी कहती है या जैसा कि लोग कहते हैं

English Usage: So the story goes, the knight defeated the dragon and rescued the princess.

Hindi Usage: जैसा कि कथा है, उस योद्धा ने ड्रैगन को हराया और राजकुमारी को बचाया।

Incidentally; by the way.

वैसे; संकेत देते हुए

English Usage: by the by, have you heard the latest news?

Hindi Usage: वैसे, क्या आपने ताज़ा खबर सुनी है?

Incidentally; by the way.

वैसे तो; वैसे

English Usage: By the bye, did you complete the report?

Hindi Usage: वैसे, क्या तुमने रिपोर्ट पूरी कर ली?