Disclaimer: This guide is for educational purposes. Electrical installations must comply with local codes (such as the NEC in the US or BS 7671 in the UK) and should be verified by a qualified electrician.
Current capacity stops the cable from melting. Voltage drop ensures your appliances actually work. Over long distances, a cable might be safe from melting, but the voltage drop might be too high.
If the surrounding air is hotter than 30°C, the cable cannot carry as much current before overheating.
When cables touch or are bundled together, they heat each other up. You must de-rate the cable.