This paper studies several issues that emerge naturally in the hydrodynamic approach to suspensions of self-driven organisms or filaments (Simha and Ramaswamy 2002 Phys. Rev. Lett. 89 058101; Kruse et al 2004 Phys. Rev. Lett. 92 078101; Hatwalne et al 2004 Phys. Rev. Lett. 92 118101). These include: a simple pictorial understanding of the instability of orientationally ordered active suspensions; the effect of translational order as well as finite geometries on these instabilities; the role of depolymerization on the possible types of alignment of active polar particles in restricted geometries; and, lastly, speculations on the relation between contractile active matter and jammed granular matter.