There are plenty of reviews describing how beautiful and wonderful the ship is.
I am reviewing solely to provide accurate technical information about the internet and telecommunications features aboard the ship, which are important for those of us who need to stay connected and who are hesitant to take a cruise vacation without knowing if we'll be knocked offline for a week. Some of us - like me - are in charge of being on call in case things at home - like servers, etc. - decide to throw a fit while we're gone.
I took an Apple iPhone (AT&T carrier - GSM) and my laptop abord the ship.
I felt Liberty's connectivity is decent.
I was able to get a good GSM cellular signal for voice calls throughout the entire voyage, provided by the onboard ship system when at sea. The carrier name showed "Cellular at SEA" and coverage throughout the ship was decent. In port, they apparently must switch the system off, and you depend on the country's signal from shore. It's sometimes hard to get a signal from an interior stateroom. Text messages were delivered promptly, both send and receive. GPRS is functional but expensive. Voice calling is latent (delays) - I experienced round trip delays between 1.0 and 2.0 seconds on voice calls. I believe AT&T hits me for $2.49/min voice calls, free incoming text if I am on a text plan, and some nominal fee for outgoing text, but I won't know until I get the bill.
I am told that CDMA phones work as well, but I didn't travel with anyone who took one aboard. (last time I took a Verizon CDMA phone aboard Splendour in 2007, I could call but couldn't send or receive text, and wondered if that had been improved since then).
Liberty's WiFi is fairly decent. I was able to sustain a video call using Skype on my laptop, and use Remote Desktop to my computer at home. The latency was surprisingly favorable for what should be a satellite connection - seemingly better than voice calling on my cell phone. The biggest caveat (arguably fair though) is that the usability of the connection is greatly influenced by the time of day, owing to the number of people onboard you are sharing it with. The connection is virtually worthless even for simple web browsing if you try right after the main dinner seating gets out, but a midnight Skype video chat is completely doable and less choppy than a calm sea. I was able to get WiFi in my room (73xx) and in most areas of the ship I tried with few exceptions (the front of the Platinum Theater got no WiFi). Time was charged by the minute - 55 cents a minute from the time you log on until the time you either log off or shut off your WiFi adapter. And billing was fair - if I turned off my WiFi without logging out, I didn't get charged for any time after I powered off.
There was an unlimited option available for $250, as well as some prepay packages at various amounts between $0 and $250 to get a rate down to as low as around 28 cents a minute (but of course you forfeit any minutes you don't use).