The fractal globule is a compact polymer state that emerges during polymer 
condensation as a result of topological constraints which prevent one region of 
the chain from passing across another one. This long-lived intermediate state 
was introduced in 1988 (Grosberg et al. 1988) and has not been observed in 
experiments or simulations until recently (Lieberman-Aiden et al. 2009). Recent 
characterization of human chromatin using a novel chromosome conformational 
capture technique brought the fractal globule into the spotlight as a structural 
model of human chromosome on the scale of up to 10 Mb (Lieberman-Aiden et al. 
2009). Here, we present the concept of the fractal globule, comparing it to 
other states of a polymer and focusing on its properties relevant for the 
biophysics of chromatin. We then discuss properties of the fractal globule that 
make it an attractive model for chromatin organization inside a cell. Next, we 
connect the fractal globule to recent studies that emphasize topological 
constraints as a primary factor driving formation of chromosomal territories. We 
discuss how theoretical predictions, made on the basis of the fractal globule 
model, can be tested experimentally. Finally, we discuss whether fractal globule 
architecture can be relevant for chromatin packing in other organisms such as 
yeast and bacteria.