Most PS Vita systems update automatically over Wi-Fi. However, manual installation via a PC or Mac is necessary in several scenarios:
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On PS Vita: Settings → System Update → Update via PC Most PS Vita systems update automatically over Wi-Fi
If you're trying to your PS Vita, you usually want 3.60 or 3.65 – not the latest 3.74. For stock updates, 3.74 is the final official firmware. 3.74 is the final official firmware.