When warlock chooses a pact with The Great Old One, he gains a feature called Awakened Mind:

Starting at 1st level, your alien knowledge gives you the ability to touch the minds of other creatures. You can communicate telepathically with any creature you can see within 30 feet of you.

My question is, is the communication two-ways, or only one-way?

I assume it's only one-way: I can "send" messages to target creature's mind but I can't receive any responses. So it's not possible for this creature to "send" me back any thoughts or messages and I can't read any of the creature's thoughts.

EDIT: As noted in the Brazol's answer, Jeremy Crawford states on his twitter, that their intent was for it to be one-way. Additionally, my concern with Awakened Mind being two-ways without any restrictions is that it would be too strong as a 1st lvl feature and could be easily abused. In the same time, making it only one-way seems to be too much of a limitation.

So I guess, the best answer to this question is:

Make a house rule that best fits your campaign.

My attempt of a solution is:

1. Make it two-ways for any friendly creatures.
2. Two-ways works like phone, it does NOT allow to read thoughts (obviously :P), only communicate something to other creature and receive a response if that creature is willing to send one.
3. Target creature can make a wisdom saving throw (vs warlock's spell save DC as in normal spell save check, ex. Wisdom saving throw in Hold Person spell) to terminate telepathical connection with warlock (hang up the phone).
4. After failing its saving throw, target creature is allowed to make another wisdom saving throw each round (or after 6 seconds) to terminate connection.

One thing I haven't decided yet is what should happen after successfull saving throw, when warlock wants to send a message again ("reconnect"). Should it be blocked for 1 round? Or maybe 1 minute? Try to image a situation when (1st lvl!) warlock is hidden behind a one-way-mirror, and is trying to "spam" some king or whoever is in the room on the other side of mirror, in an attempt to drive him mad. Wisdom saving throw should protect a creature from that kind of "thoughts spam". Don't you think?

Also keep in mind this quote (by ZHDarkstar):

Some NPCs may react violently against the telepathic intrusion, while others might run in fear.

For reference: the same problem is disputed on the wizards forums (ZHDarkstar quote taken from there).