If it's in the past, it's not current. If it's out of date, out of style, or out of time, it's not current. If it's up-to-the-minute, right now, and in the present, it is current.
Origins of the word current all point to the meaning "present." Things that are current are happening now; they are part of the present time. News reporting looks at "current affairs" because past affairs are no longer news; they are history. Expressions like "staying current" or "keeping up with current events" show a need or desire to know what's popular, important, or relevant now. As a noun, a current can be a flow of water, electricity, or ideas.