At the small end were bendable displays in the 6-inch (152mm) LG G Flex phone and in the 5.7-inch (145mm) Samsung Galaxy Round.
At the large end, is a genre that has come out of the blue: bendable TVs - a 77-inch (2m) demonstrator from LG and 85-inch (2.2m) demonstrator from Samsung.
Why would anyone want a bendable TV?
The idea has come from curved TVs, which appeared only recently to improve large-screen TV viewing experience.
"The curved screen gives videos a presence not felt on flat screens whilst a wider field of view creates a panoramic effect that makes the display seem even bigger than it is. The TV screen appears as if it is floating above the metal frame," said Samsung. "The design creates improved viewing angles and higher contrast from different viewing positions. To maximise the advantages, Samsung has developed the optimal curvature, 4200R, which provides the best picture quality from a normal watching distance of 3-4m."
However, huge curved screens suit a single central viewer, or a tight cluster of viewers. If people are spread around a room, a flat screen is a better option.
As making the flat/curved decision could put people off committing one way or the other, why not make TVs that will bend their own screens at the touch of a button.
"The range of curvature was determined by taking into account key factors that affect the viewing experience such as screen size and viewing distance,” said LG.
The idea is that by adjusting the curvature, the viewer can tailor the TV viewing angle to their tastes.
"The Flexible OLED TV has been subject to tens of thousands of hours of tests to ensure the reliability and durability," said LG.
Alongside bendable display TVs, the two companies also competed with very large permanently-curved screen TVs at CES.
LG showed a 105-inch (2.7m) curved TV with an extremely wide screen 21:9 aspect ratio.
With 11 million pixels (5120x2160), screen resolution is greater than the '4K' TV standard.
Called 105UC9, the TV uses an LCD rather than an OLED display.
"The 105UC9 represents the collaboration between LG Electronics and LG Display. Until now, OLED panels were preferred for curved displays due to their ability to generate their own light. LG Display overcame the challenge of uneven backlighting by refining its TFT pixel circuit technology to prevent colour leakage and to ensure a superior viewing from virtually any angle," said LG. "New technology was introduced to maintaining structural integrity across such a large screen."
Why so wide?
"An advantage of the extra-wide screen is that it enables users to access viewing information on the side of the screen without blocking any of the ongoing action," said the firm.
Samsung's largest curved TV, the U9500, has a very similar specification: 21 x 9 aspect ratio executed with 11 million pixels in a 5,120 x 2,160 array.
This one can be wall-mounted with "the specially designed kit, compatible with VESA Standards", said Samsung.
At the 2013 IFA show in Berlin, Samsung revealed a 1.4m curved OLED model, and made interesting use of the available pixel speed with something it calls 'Multi-View'.
"Two people can watch two different channels at the same time on the same screen using Multi-View glasses that come with ear buds for stereo sound," said Samsung. "This feature, made possible by an exceptional refresh rate, is so advanced that viewers can watch any combination of 2D and 3D content simultaneously."
The mightiest TV screen Electronics Weekly was aware of at CES 2014 was Samsung's 110-inch (2.8m) S9 flat screen demonstrator.
"Using compression frame technology, the frame is a strong and stable in structure, yet slim and sleek," said Samsung. "Frame TV eschews the squared black bezel and conventional neck stand."
Down at the small end, Samsung and LG were showing curved phones, aimed at production rather than just demonstrating capability.
LG's G Flex has a 1,280x720 bendable plastic 6-inch OLED display and really is slightly flexible. Flexibility is there to add durability and the company discourages frequent voluntary flexing.
"The ultra-thin, ultra-light flexible OLED display and curved OLED panel are built on plastic substrates instead of glass, giving LG G Flex its unique shape and durability," said LG. "The curved battery is designed with LG Chem’s patented stack-and-folding technology, which reduces the physical stress on the battery pack when in the curved form." Capacity is 3,500mAh.
Another unusual feature of this phone is that the back panel has a 'self-healing' plastic surface, on which small scratches disappear of their own accord.
Unlike the G Flex, Samsung's Galaxy Round is not actually a flexible phone, but it does use a bendable OLED, 1080p this time, for its curved display.
While G Flex is curved like a banana, Galaxy Round is curved like celery.
Both companies claim their phone fits the face and back pocket better than flat phones.
"The vertically curved design of the LG G Flex reduces the distance between one’s mouth to the microphone when the device is held against the ear, as traditional telephone handsets used to. The curved form increases the sound level by 3dB compared to typical flat smartphones," claimed LG. "In landscape mode, the display offers an immersive, cinematic experience, with the result being the most comfortable viewing angle for watching videos or playing games."