At one point, we wrote a lesson on the difference between eröffnen and öffnen. The verb öffnen is basically what it sounds like, while the verb eröffnen can also be used with non-physical entities that can be "opened," as well as something that is established or instituted.

When it comes to closing something, you probably know the word schließen. And just as aufmachen can substitute for öffnen, zumachen is another verb used to talk about closing something. 

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Jetzt schließe ich meinen Koffer.

Now, I'll close my suitcase.

Caption 22, Christiane: fährt in den Urlaub

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Die Polizei sagt, er solle seinen Kofferraum aufmachen.

The police officer says he should open his trunk.

Caption 4, Sabine erzählt Witze: Die Pinguine

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Wenn keine Tür da ist, kann man sie auch nicht zumachen.

If there is no door, you can't close it either.

Caption 26, Piggeldy und Frederick: Haus

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That is all relatively simple, but when it comes to locking and unlocking something like a door, there are many more verbs you can use, such as aufschließen, zuschließen, verschließen, and abschließen. The first two are similar to aufmachen and zumachen, but would refer to something that is shut very securely or locked. You may know the verb abschließen as "to finish" or "to conclude," but it can also mean "to lock up." Interestingly, aufgeschlossen is also an adjective used to describe a person being "open" or "receptive."

Frankreich plant nachzuziehen und auch London will aufschließen.

France plans to follow suit and London wants to open [its financial markets] up as well.

Caption 41, Frankfurt wird Handelszentrum für die chinesische Währung Yuan

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Die Schachtel ist total sicher verschlossen.

The box is completely and securely shut.

Caption 58, The Simple Physics: Schrödingers Katze

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Also, die Leute sind sehr aufgeschlossen.

Well, the people are very receptive.

Caption 7, Eva Croissant: Interview

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It then gets even more specific, with verbs like entriegeln and entsperren, which could also mean "unlatch" or "unbolt." 

Maik gibt den vierstelligen Code ein und entriegelt das Schloss.

Maik enters the four-digit code and unlocks the lock.

Caption 28, Fußballspieler Maik Franz: "Call a Bike"

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Further Learning
You can find many examples of these verbs on Yabla German, which is the best way to understand the nuances in their meaning. You can also look up the list of possible translations for each verb with an online dictionary like leo.org to get a sense of this as well. While you're at it, consider aufsperren and zusperren, two additional verbs more often used in Southern Germany. Based on the other verbs you have learned, what do you think these mean?