Vitex agnus-castus AKA Chaste tree, Monks' Pepper, Summer lilac. Mine's not quite blooming yet.

The second appears to be more of a bush. They're are three of them in the picture below, under the crape myrtles. They have a leaf that is kind of waxy like a holly leaf. It also has started blooming with a red flower.

Looks like some kind of pomegranate. Might be the edible kind. There are also ornamental pomegranates that make small fruits but they don't taste good.

Thanks Annie! It's a new house for us, so I'm trying to educate myself on caring for the landscaping. I'll do some research based on your identifications, but if you happen to have any tips for care of other of these guys, I'm definitely open to it. From my uneducated perspective, it feels like both may need to be trimmed/pruned?

Thanks again!

Right now the Vitex is a) in beautiful bloom b) a good plant for bees and butterflies and c) adding some nice screening for that hulk of a house on the other side of the fence. I don't know where you live, but here in Austin the vitex shrubs/trees lose their leaves and go dormant in winter so usually late winter or very early spring is the best time to shape and prune them. Since they produce the next year's flowers on new growth you will still get blooms.

Those pomegranates look pretty short so might be young or maybe the previous owner was keeping them pruned as large shrubs rather than trees. They may also have been put in as screening plants.

It won't hurt to watch and wait while you learn what you have and see what the sun/shade patterns are and how they change with seasons, locations of cold spots or heat traps, etc. My pomegranate has too much shade so we seldom get fruit but you might be lucky. I think they produce fruit on second year branches but am not sure - bet someone on here will know! Good luck!