Especially in sitcoms men are made out to be slackers when it comes to doing the housework. There is a belief that men don't help out as much with the kids and don't pull their weight when it comes to doing their share of the housework.
Does this still hold up in modern times? Have their been any recent studies into the split of housework and whether men spend equal time with children?
The short answer is yes, women do more housework than men, but it's shifting in the direction of more equal distribution of labor. There's a fantastic and well-referenced summary of current understanding on Po Bronson's site.
According to The Journal of Marriage and Family in 2002, women do more housework than men, but not all of it by any means. (See this graph of the results by country.)
Much more detail can be found in this article from the Marriage and Family Encyclopedia, which suggests that since the first major studies in the 1970s, men have been taking on more of the housework, although women still do more than men in most households.
According to an article from 2000:
Household work continues to be divided according to gender, with women performing the vast majority of the repetitive indoor housework tasks and men performing occasional outdoor tasks
Taken from: Coltrane, S. (2000). "Research on Household Labor: Modeling and Measuring the Social Embeddedness of Routine Family Work." Journal of Marriage and the Family 62:1208–1233.
Similar information can be found from Philip N. Cohen, Suzanne M. Bianchi et al., Crompton Rosemary and Lyonette Clare, and many others.
definitely, yes. Using the ATUS (American) data 2003-2019, in this paper the gap we have is: 
The gap between women and men in total housework time is still a little over an hour every day.
