Older machines
Due to the nature of Blu-ray drives, they will only work on computers that support SATA format. SATA format replaced the previous Parallel ATA format around 2003, and is mostly associated with hard drives. For the most part, SATA allows for faster data transfers, and also is more energy efficient. Double-check the make and model of your computer to ensure that it will accept this format before purchasing any Blu-ray player or burner. For the most part, if your computer was made in the past 4 years, chances are that you can support a Blu-ray drive. Any older than that, and it's possible that you have the old format. It's better to make sure beforehand instead of realizing you need a whole new computer in order to experience Blu-ray.
Processing Power
Dual-core processing technology is the minimum requirement for experiencing Blu-ray. For best results, consider quad-core instead. Anything less than Dual-core can cause severe slowdown, as Blu-ray requires a lot of resources in order to display its high-definition picture. Processor upgrades are possible for older machines, but dual-core may not be supported. Check with the make and model of your computer and see what upgradeable options there are, if there are any. Unfortunately for laptop users, most if not all laptops have processors integrated directly into the motherboard, so an upgrade there is highly unlikely. On top of that, upgrading processors can be expensive, as dual-core processors range from $45 to $300, while quad-core ranges from $200 to $570.