We discuss some aspects of spatiotemporal chaos in a family of one-dimensional PDEs including the Kuramoto-Sivashinsky (KS) equation, with particular attention to the importance of large spatial scales. We shall see that these long-wave modes act as a "heat bath" in the KS equation and maintain the spatiotemporal disorder. Addition of a destabilizing term at large scales induces a bifurcation sequence to an attracting shock-like solution; this observation has had interesting implications for the estimation of analytical bounds on the attractor. The main part of our story concerns relatively recent (ongoing) exciting developments on a sixth-order analogue of the KS equation, the Nikolaevskii equation. In this equation, which arises via the coupling of unstable short-wave modes with a neutrally stable long-wave mode, one observes a spatiotemporally chaotic state with strong scale separation. As such, a multiple-scale asymptotic description would seem to be in order, but as observed by Matthews and Cox, the asymptotically consistent scaling for the dynamics is different from the Ginzburg-Landau scaling one typically observes at onset. However, our computations indicate the need for corrections to the Matthews-Cox scaling hypothesis, and we infer the existence of a novel spatiotemporally complex attractor with different scaling regimes.