I have read in several places that people in the past were on average substantiality shorter than the average person today. For example it is estimated than the average soldier in Greco-Persian wars was only 5'4" (Thanks Dan Carlin). That seems really short to me. Was this due malnutrition or disease? Or are just that because tallness is considered a desirable trait in many cultures, so we are just descended from the taller people. Thanks!
Precisely nutrition and disease. If you search for histories of public health there is a tremendous amount of material on human height and bodymass, and what's interesting is that you don't have to go back to antiquity to show it.
People on average were relatively short until sanitation and access to nutrition improved in the nineteenth century. There are, in fact, plenty of accounts from the UK as recently as the early twentieth century which comment on the small stature of underfed miners and labourers in industrial towns.
What's interesting is you can now see the process repeating in the 'developing' world. The past fifty years have revealed that in as few as two generations, people from countries often considered relatively short by genetic determination, such as China, grow to the same average height as Westerners under the same conditions. I have no doubt the process is repeating itself across India, Pakistan, and South East Asia.
You do raise a good point about sexual selection, and height is seen as a desirable trait, but to what degree this affects average heights is hard to determine. As far as I know that element hasn't really been covered in public health literature. It has been shown, however, that we are getting taller (and unfortunately, wider) year on year.