  We consider three aspects of avoiding large squares in infinite binary words.
First, we construct an infinite binary word avoiding both cubes xxx and squares
yy with |y| >= 4; our construction is somewhat simpler than the original
construction of Dekking. Second, we construct an infinite binary word avoiding
all squares except 00, 11, and 0101; our construction is somewhat simpler than
the original construction of Fraenkel and Simpson. In both cases, we also show
how to modify our construction to obtain exponentially many words of length n
with the given avoidance properties. Finally, we answer an open question of
Prodinger and Urbanek from 1979 by demonstrating the existence of two infinite
binary words, each avoiding arbitrarily large squares, such that their perfect
shuffle has arbitrarily large squares.
