Recent theoretical and experimental progress on
the study of ferrotoroidic materials is reviewed. The basic
field equations are first described and then the expressions
for magnetic toroidal moment and toroidization are derived.
Relevant materials and experimental observation of
magnetic toroidal moment and toroidal domains are summarized
next. The thermodynamics of such magnetic materials
is discussed in detail with examples of ferrorotoidic
phase transition studied using Landau modelling. Specifically,
an example of application of Landau modelling to
the study of toroidocaloric effect is also provided. Recent
results of polar nanostructures with electrical toroidal moment
are finally reviewed.