For $Y \to Z$ a morphism of pointed ∞-groupoids and $X \to Y$ its homotopy fiber, there is a long exact sequence of homotopy groups
In terms of presentations this means:
for $Y \to Z$ a fibration in the ordinary model structure on topological spaces or in the model structure on simplicial sets, and for $X \to Y$ the ordinary fiber of topological spaces or simplicial sets, respectively, we have such a long exact sequence.
For background and details see fibration sequence.
Given a tower of homotopy fibers such as a Whitehead tower or Adams resolution, the long exact sequences of homotopy groups for each stage combine to yield an exact couple. The corresponding spectral sequence is the Adams spectral sequence.