Seed collecting, hybrids?

Seed collecting, hybrids?

In regards to seed collecting from plants in the garden, does the fact that a plant is labeled as an "F1 hybrid" have any bearing on wether or not the seeds collected from that plant will produce? See I was given some petunias last Spring, and they weren't "Wave" brand petunias but a similar behaving type called "Madness". On the care tag with the plant id and all it says "F1 Hybrid" and I vaguely remember reading or hearing about hybrids and seed collecting and maybe there was something about the seeds being sterile. I'm not looking for an exact replica of the parent plant, just something that possibly behaves in a similar fashion, regardless of color, spread, what have you. Just wondering if I can expect something to even grow from the seeds.
Sharing Some Garden Pron

Sharing Some Garden Pron

Caterpillar and plant IDs

Caterpillar and plant IDs

Plant Identity

Plant Identity

Late July Garden, Zone 7

Late July Garden, Zone 7

I conquered Ikea all by myself

I conquered Ikea all by myself

My closet is NOT included

My closet is NOT included