Will Blu-Ray DVD’s play on a regular old DVD player?

I have a 4 year old DVD player that I don't think is HD and certainly not Blu-Ray. It plays regular Netflix movies fine, but since the industry is changing to Blu-Ray, will they play on my "regular" unit or do I have to go out and buy a new one?
Also, will home movies I had put on DVD play on a new Blu-Ray?

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