Spacetime properties of (1,0) string vacua

We discuss one of the generic spacetime consequences of having (1,0) worldsheet supersymmetry in tachyon-free string theory, namely the appearance of a ``misaligned supersymmetry'' in the corresponding spacetime spectrum. Misaligned supersymmetry is a universal property of (1,0) string vacua which describes how the arrangement of bosonic and fermionic states at all string energy levels conspires to preserve finite string amplitudes, even in the absence of full spacetime supersymmetry. Misaligned supersymmetry also constrains the degree to which spacetime supersymmetry can be broken without breaking modular invariance, and is responsible for the vanishing of various mass supertraces evaluated over the infinite string spectrum. [Talk delivered at Strings '95, based on material drawn from hep-th/9402006 and hep-th/9409114. To appear in Proceedings.