All Blu-ray and 4K UHD Blu-ray players are designed to be backward compatible with your existing DVDs. Most will also upscale DVD to 1080p (or 4K), which will mean a boost in image quality when played on a flatscreen TV.
If you have DVDs from other regions — e.g., you live in the UK and have Japanese DVDs — you will need to check with the manufacturer to make sure your player is compatible.