Additivities of the families of Darboux-like functions

It is well known that every continuous function from $\mathbb{R}$ to $\mathbb{R}$ maps connected sets to connected sets. However, the converse is not true in general, that is, the family of real functions that map connected sets to connected sets (known as Darboux functions) strictly contains the family of continuous functions. This method of considering necessary but not sufficient conditions for continuous functions lead us to obtain the families of functions known as Darboux-like functions.  In this expository paper we will study the main results related to the inclusions and set operations between the classical families of Darboux-like functions, and also analyze the cardinal coefficient known as additivity of these families.