If you use lithium-ion batteries to power your projects, make sure you charge the batteries as per the manufacturers specifications.
Use approved wallwarts for those applications that require constant power.
All in all, these projects are 'no' more likely to catch fire than a transistor radio is.
When operating high voltage/current devices with relays etc., you must observe your electrical regulations.
High current low voltage projects (example: 5V at 20amp LEDs) must be properly designed.
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