Surf travel really didn't catch on with the general public until the 60's, and not with any kind of serious volume until the 80's. In fact, during the earliest surf-related travels of Duke Kahanamoku (after the turn of the last century) he often waited until he got to a location, then made a new board for himself!
The 60's saw worldwide jet travel explode along with the popularity of surfing...but dragging a 10 ft long board on board an overseas flight was hard. The airlines weren't oriented to dealing with sporting accoutrement at that time, and boards were awkward on top of that.
Enter Mr. Karl Pope. He developed the Tri-Sect surfboard in 1964, then formed Morey-Pope with Tom Morey to produce them. The Tri-sect wasn't a resounding success, mainly due to the weight increase of already heavy longboards. But the idea was sound, and Karl came back in the 90's with Bi-Sect boards which were weight friendly.
The El-Paipo print ad from 1970 really struck a chord with the new generation of shortboard surfers. In fact, in recent years I've heard a lot of people say that this is the best ad ever published in Surfer Magazine. What a timeless sense of adventure it evokes!
Of course, mats have always occupied the top rung of the ladder when it came to compact surf travel. I remember being disappointed at how un-surfy my dad's car looked when we had mats in the trunk. I wanted boards on the roof, dammit! And when Boogies surfaced in 1974, a lot kids had their parents lash them on top of the car to address their need for public identity.
Please post your mat travel stories in the comments section...and if you have photos, send them to me at firstname.lastname@example.org !