The quick overview is that the 2015 Millenial uses multiple devices, but is the same person. Behavioral patterns on the laptop, phone, tablet, work computer etc all combine to form a single addressable consumer. If you look at a pair of pants at home, the marketer doesn't care that you're on your phone - they want to target you with those same pants.
But that's easier said than done. How do they know that your phone represents the same exact person? That's where companies like TapAd (probably the market leader), Drawbrid.ge and others come in. This market is fragmented using "deterministic" and "probabilistic" matching technologies. Deterministic means a piece of data that is [more or less] definitely correct for matching a user. For example, your email address, credit card, or other information. Tapad loves this stuff, so they have deals with a number of websites, apps, etc to collect as much of the deterministic-style data as possible. TripleLift does not directly participate in this market, but instead relies on partners like Tapad and Drawbrid.ge.
Probabilistic data, on the other hand, is data that "probably" matches a user. If you get to a high enough confidence, for enough users, you'll likely get good enough results. This uses things like location data, behavioral patterns, IP data - things like whether devices regularly appear on the same WiFi etc, Tapad also uses probabilistic data to expand their deterministic models. TripleLift also does not play in this market.
Facebook and Google are the undisputed champs. They have your login information almost everywhere, and this is what powers the Facebook Audience Network and is a big piece of the Google Display Network. Amazon is likely getting there, and companies like Pandora, Spotify and others have a good amount of relevant data.
The most surprising part of cross-device is that the browser in your phone is considered a separate device from apps. This is because they don't share any data, IDs, or other information that could tie them together. So a big challenge is actually unifying the same exact device.
Given the complexity of this space, as well as the murky PII and opt-out questions, TripleLift won't be building an in-house solution. We do expect to partner with the players that focus on this data.