Here are some complex twists used in Liy:

TL-ssk - twist left (1 over 1), ssk second (front) stitch with next stitch:

(see the video on YouTube here)

T2out1-inc1 - twist 2 stitches outwards over 1 (in both directions), increasing 1:

(see the video on YouTube here)

TLsl2-m1L-btwn - twist left, slip both, make 1 left between the stitches:

(see the video on YouTube here)

Below are some complex twists used in Adventure Knitting 3:
T2out2-inc1, T2in2-dec1, and TLR, all from the Sasquatch pattern.
(Twist stitches apart & together are separate, since they're more like cables.)
Check out the twisted stitches page to see how I do my regular twisted stitches.

T2out2-inc1 - twist 2 stitches each outwards over 2, increasing out from 1 center stitch:

(see the video on YouTube here)

T2in2-dec1 - twist 2 stitches each inwards over 2, knit them together to decrease 1 and create 1 center stitch:

(see the video on YouTube here)

TLR - start to work a TL partway, then work that top stitch into a TR with the third stitch:

(see the video on YouTube here)

T2out2-inc1

twist 2 stitches outwards over 2, increasing 1 from the center - start by slipping 2

lift the lower stitch below the next stitch...

...up onto left-hand needle, so that it's positioned correctly, with the right side of the loop in front on the needle

slip the 2 stitches back to the left-hand needle

work a twist right 1 over 2 stitches, by first slipping 3 stitches as if to knit 3 together...

...then slipping them back to the left-hand needle, straight over so they are twisted

knit the first (front) stitch through the back loop

knit the next 2 (back) stitches through the back loops

work a twist left 1 over 2 stitches, by first slipping each of the next 3 stitches, all knitwise

slip those 3 stitches back to the left-hand needle, twisted, by sticking the needle point through all 3 stitches at once, so that the two needles are pointing in the same direction

knit the 3 stitches

T2in2-dec1

twist 2 stitches each inwards over 2, decreasing them together in the center - start by first slipping each of the next 3 stitches, all knitwise

slip those 3 stitches back to the left-hand needle, twisted, by sticking the needle point through all 3 stitches at once, so that the two needles are pointing in the same direction

knit the first 2 (back) stitches...

...and slip the third stitch - so you've worked a TL2 twist, but with the front stitch slipped

begin to work TR2 by first slipping 3 stitches as if to knit 3 together...

...then slipping them back to the left-hand needle, straight over so they are twisted

if you twisted them this way, you need to reposition the front stitch so that it's sitting correctly on the needle, with the right side of the loop in front

slip the stitch from the right-hand needle back to the left

work a k2tog decrease (knitting together the 2 front sts, from the outsides)

knit 2 stitches (the back stitches from the TR2 twist)