Are there recent theories on physiognomy? What are recent theories on the relation between personality and facial or body shape, and are there studies to support them?

See Wikipedia on physiognomy and somatotypes &amp; constitutional psychology for background.

I would be most happy if you could go beyond the well-known facts about intelligence and beauty.
Facial shape



Aggression relates to facial width-to-height ratio (Carré, McCormick, &amp; Mondloch, 2009; Carré &amp; McCormick, 2008). The width-to-height ratio is the distance between the left and right zygion (the outside of the cheek bone) divided by the distance between the top of the upper lip and the mid-brow. Here's a useful image displaying the meaning of this ratio from the 2009 article:


  


Carré et al. found that the lower the width-to-height ratio, i.e. the shorter the distance between lip and brow in relation to the distance from cheekbone to cheekbone, the more aggressive the person is (as measured through a well-validated laboratory task) and is perceived by strangers.

Also, the Big Five differ in observability (Penton-Voak, Pound, Little, &amp; Perrett, 2006). Participants were asked to rate the Big 5 aspects of the personality of strangers. There was a strong agreement between these ratings and the results of a personality test the depicted persons had filled in (reliability calculated as Cronbach's $\alpha=.70\text{–}.89$ for all dimensions, only male conscientiousness was $.63)$. Similar results were found with composite images.

Here are some composite facial images from that article:


  
  


Differences are subtle, but perceptible! BTW, I think I came across this from The Personality Puzzle (Funder, 1997) originally, but I'm not 100% certain.

Some of these facial differences may relate to testosterone. Dominance and masculinity relate to perceptible differences in male facial shape due to the prenatal influence of testosterone, but fortunately for the scope of this answer, these differences do not affect attractiveness to females (Neave, Laing, Fink, &amp; Manning, 2003; Swaddle &amp; Reierson, 2002).



Body shape



Body mass index

There is some evidence that body mass index (BMI) relates to higher extraversion and psychoticism and lower neuroticism in middle-aged Japanese people (Kakizaki et al., 2008), impulsivity (Murphy, Stojek, &amp; MacKillop, 2014; first citation of the new year!), hypomania (Valenti, Omizo, &amp; Mehl-Madrona, 2011), and worse cognitive executive functioning (Gunstad et al., 2007). However, one study did not find a relationship between BMI and personality psychopathology (Picot &amp; Lilenfeld, 2003). Another study found a positive relationship between neuroticism and BMI in middle-aged American women only (the opposite of the relationship in the Japanese population according to Kakizaki et al., who did not mention prominent sex differences) and extraversion among men only (same direction as in Kakizaki et al., but again, more sex differences), as well as negative relationships with openness, agreeableness, and conscientiousness (Brummett et al., 2006). Low conscientiousness related more strongly to BMI in women, and predicted BMI increases over time.

Testosterone

Another set of correlations between personality and body shape are mediated by testosterone, which affects several, readily observable, physical characteristics, including muscle mass, bone length, vocal pitch and tone, hair growth patterns, body odor, dermal oil secretion and acne, subcutaneous facial fat and facial bone contours, and prominence of the Adam's apple. Testosterone relates to many behavioral patterns in romantic relations, the general trend being toward more competitive promiscuity and less long-term fidelity with increasing testosterone (e.g., Burnham et al., 2003). Testosterone increases in men anticipating competition, but may decrease in women (Mazur, Susman, &amp; Edelbrock, 1997). This effect may be moderated by implicit power motivation (Schultheiss, Campbell, &amp; McClelland, 1999); if so, it's conceivable that personality could affect appearance over time by altering testosterone levels. Power motivation interacts in complex ways with sex and the outcome of social contexts in affecting testosterone (Schultheiss et al., 2005; Schultheiss, Wirth, &amp; Stanton, 2004).

One of the underlying personality differences associated with testosterone appears to be in sexual motivation, which manifests in non-human animals as well. Testosterone also relates to sensation-seeking (Roberti, 2004; Gerra et al., 1999; Daitzman &amp; Zuckerman, 1980; Zuckerman, Buchsbaum, &amp; Murphy, 1980) and risk tolerance (Sapienza, Zingales, &amp; Maestripieri, 2009; Stanton et al., 2011; Stanton, Liening, &amp; Schultheiss, 2011), though the relationship exhibits some complexities across domains of risk (Stenstrom, Saad, Nepomuceno, &amp; Mendenhall, 2011). The relationship between testosterone and risk aversion may be mediated by abstract reasoning ability (Brañas-Garza &amp; Rustichini, 2011). 

Testosterone also relates to dominance (Mazur &amp; Booth, 1998), aggression (Archer, 2006; Birger et al., 2003; Ehrenkranz, Bliss, &amp; Sheard, 1974; Archer, Birring, &amp; Wu, 1998), and lack of empathy, the last of which appears to be an empirically established effect of testosterone (Chapman et al., 2006; Knickmeyer, Baron-Cohen, Raggatt, Taylor, &amp; Hackett, 2006; van Honk et al., 2011; Ronay &amp; Carney, 2013; see also Auyeung &amp; Baron-Cohen, 2013). Testosterone may even explain deficits in social development (Knickmeyer &amp; Baron-Cohen, 2006) and autistic traits in general (Auyeung et al., 2009; Ingudomnukul, Baron-Cohen, Wheelwright, &amp; Knickmeyer, 2007), according to a theory that conceptualizes autism as extreme cognitive maleness (Baron-Cohen, 2002; Baron-Cohen, Knickmeyer, &amp; Belmonte, 2005; Chakrabarti et al., 2009).

Testosterone relates positively to emotional arousal and anger, but also relates positively to attentiveness to angry facial expressions in others (van Honk et al., 1999). This latter result demonstrates that testosterone doesn't unilaterally decrease awareness of others' emotional states, especially to whatever extent they pose immediate threat. The relationship between testosterone and antisocial behavior is also moderated by socioeconomic status (Dabbs &amp; Morris, 1990). These complexities may limit the otherwise impressive relationships between personality and testosterone.

In women, estradiol may instead play a similar role to testosterone in men, modifying dominance motivation (Stanton &amp; Schultheiss, 2009). Wikipedia lists some observable physiological effects of estradiol, but these claims currently lack supporting citations.



References (there's a ton; I recommend zooming in with Ctrl++ or copy-pasting into a word processor)

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&middot; Valenti, M. P., Omizo, M. M., &amp; Mehl-Madrona, L. (2011). Personality and obese Body Mass Index. The New School Psychology Bulletin, 9(1), 34–38. Retrieved from http://www.nspb.net/index.php/nspb/article/viewFile/204/294.
&middot; van Honk, J., Schutter, D. J., Bos, P. A., Kruijt, A. W., Lentjes, E. G., &amp; Baron-Cohen, S. (2011). Testosterone administration impairs cognitive empathy in women depending on second-to-fourth digit ratio. Proceedings of the National Academy of Sciences, 108(8), 3448–3452. Retrieved from http://www.researchgate.net/publication/49817064_Testosterone_administration_impairs_cognitive_empathy_in_women_depending_on_second-to-fourth_digit_ratio/file/d912f50b5d773ca9e0.pdf.
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&middot; Zuckerman, M., Buchsbaum, M. S., &amp; Murphy, D. L. (1980). Sensation seeking and its biological correlates. Psychological Bulletin, 88(1), 187–214.