The short answer
Almost everything about your child is a mix of both biological parents. Most genes come in two copies, one inherited from each parent, so most traits draw on both sides of the family.
There are two real exceptions, and both follow the egg: the mitochondria, and the X chromosome of a child with XY chromosomes. Many popular claims about traits coming from one parent, such as intelligence from the mother, do not hold up.
Mitochondria come only from the egg
Mitochondria are tiny structures in each cell that turn molecules into energy. Each one holds a small amount of its own DNA.
Only egg cells pass mitochondria on to the developing embryo. So mitochondrial DNA always comes from the biological parent who provides the egg, never from the sperm. This is also known as maternal inheritance.
Conditions caused by changes in mitochondrial DNA can affect children of any sex. They can appear in every generation of a family, but they are not passed on through the sperm.
The X chromosome follows the egg for XY children
Most people have either two X chromosomes (XX) or one X and one Y (XY). One X is always inherited from the biological parent who provides the egg. A child with XX chromosomes gets a second X from the sperm. A child with XY chromosomes has only the X from the egg.
That has a clear effect on traits carried on the X chromosome, called X-linked traits. They cannot pass through the sperm to an XY child.
Colour blindness is the best-known example. An XY child has only one X, so a single copy of the variant is enough for it to show. An XX child has a second X, and a variant there usually needs to be on both copies to have an effect. That is why colour blindness is more common in males than in females, and why a parent with XX chromosomes can carry the variant without being colour blind and still pass it on.
Myth: intelligence comes from the mother
A popular claim says that children get their intelligence from the mother. Research does not support a rule like that.
MedlinePlus Genetics describes intelligence as a complex trait shaped by both genes and environment. It likely involves many genes that each make only a small contribution, and studies have not found any single gene with a major role. Intelligence is also strongly influenced by the environment.
When a child is like one parent, it may be down to the genes they share, to the home they grew up in, or, most likely, to both. With many genes involved, and a copy of most genes from each biological parent, there is no reason to credit one side alone.
Myth: baldness comes from the mother's father
This one has a grain of truth. The gene with the strongest known link to male pattern baldness is the androgen receptor gene (AR), and it sits on the X chromosome. An XY child gets that X from the biological parent who provides the egg. That parent got it from one of their own two parents, so either grandparent on that side could be the source.
But it is far from the whole story. A 2017 study of more than 52,000 men in the UK Biobank found 287 independent genetic signals linked to male pattern baldness. Forty were on the X chromosome. The other 247 were on the other chromosomes, which children inherit from both biological parents.
So baldness on either side of the family can play a part, and no single grandparent decides it.
Height and most other traits come from both
Height shows how most traits work. MedlinePlus Genetics estimates that about 80% of a person's height is determined by the DNA variations they inherited. More than 700 of those variants have been found so far, and more are expected. Environment, such as nutrition, makes a smaller contribution.
Because children inherit those variants from both parents, they usually grow to be about as tall as their parents. That is why the child height predictor starts from both biological parents' heights. Our eye colour calculator and blood type calculator work the same way: each parent passes on one of their two copies.
What this means for your baby's looks
Looks are a mix too. Your child's features draw on genes from both of you, and each of you passes on only one of your two copies of each gene. Nobody can tell from your faces which copies those will be, or which side your baby will take after.
If you are curious, the AI baby photo generator blends your two photos into a picture of a possible child. It is a fun way to imagine it, not a genetic prediction.