Notifications and alerts work by sending a message or email to your device when motion or sound has occurred. This feature is only found in the Wi-Fi monitors, and isn't the best feature for baby because it comes after the fact (sometimes up to 30 min or more after), it does not offer details of the type of sound or motion detected, and could get annoying with useless and excessive messages being sent. In the end, we prefer sound activation over notifications and feel that alerts and notifications aren't all that useful for keeping tabs on your baby.
The first thing you need to consider is whether you want to have an audio-only baby monitor or one that incorporates video. Some parents choose to use smart home security cameras that send a video feed and alerts to their phones via an internet connection instead. Your choice largely depends on your budget and how high tech you want the baby monitor to be.
Watching your child from moment to moment is far more important than going over footage from previous nights, so baby monitors don't usually make a big deal about saving video for later, whether using built-in storage or through a cloud service. They can take snapshots and short clips when they detect movement, but they won't offer time-lapse videos of entire nights at once, or let you page through hours or days of footage. Those features are useful for identifying burglars, but they don't really help you watch your child unless you're in a Paranormal Activity sequel.

It may surprise you to hear that simply being able to last through the night, unplugged, with the display off, qualifies as exceptional battery life for a baby monitor. The Infant Optics was one of the only monitors in our testing that could easily do that, and then last a while longer the next day before needing a charge. (The manufacturer claims it lasts 10 hours with the display off—we got that amount of time off a full charge, even when checking the display intermittently.) This model also charges via a USB connection, which actually sets it apart from a variety of competitors, some of which use ineffective and inconvenient proprietary DC chargers or even disposable batteries.
Your phone might not have great battery life. Many parents who use a wifi baby monitor come to the realization that their smart phone battery life isn't so great when they are streaming a live video and audio feed from their baby monitor. If you have a newer iPhone or Android device, it will probably do pretty well, but if you have an older phone the batter is probably a bit weaker already and you will notice your battery life dropping pretty quickly during use. So definitely consider battery life and charging options for your smart phone when you are choosing between a self-contained versus wifi baby monitor. 
But, for many parents, a baby monitor is a part of daily life. If you need to visually confirm that your baby is safely asleep for the night in order to leave the room and relax, it can feel like a necessity. A baby monitor gives you a camera and/or microphone near the crib, and a separate rechargeable parent unit (aka, a monitor) that connects wirelessly and can travel with you throughout the house, either working while plugged in or running off its battery. Monitors are most commonly used for new babies, but even once your household is past the infant stage you may appreciate an easy way to check to make sure your kid is still asleep, still breathing, or still in the room at all. It’s nice to see your children in bed, dreaming happily, sleeping in adorable new positions, cuddling with animals, and generally doing okay. A baby monitor can make that happen.

Wi-fi baby monitors are the latest innovation in high-tech baby gear, and they’re super convenient. A baby monitor with wi-fi allows you to connect anywhere that has Internet service or Bluetooth capability, and the monitor can often be controlled remotely using a smartphone or computer. This functionality makes the wi-fi baby monitor great for travelling (unless you’re heading to a remote location). Safety tip: No matter what connection you use, be sure that it’s a secure connection in order to prevent your monitor from being hacked.
We tested monitors daily over a period of several months, in three houses: one nearly 100 years old with plaster walls, plus a newer home with standard drywall construction, and a two-level 1960s home with a driveway on another level from the kids’ rooms. We tried the cloud-based monitors with two routers to be sure that any connection issues were with the monitors themselves and not the Internet connection.
To save on battery life, some audio/video models only turn on when the baby makes an unusual motion or sound. Some models come with a motion-detector pad that fits under the crib sheet. This type of motion sensor is intended to prevent SIDS. Sensitive enough to detect changes in breathing, an alarm sounds if there is no movement after 20 minutes. However, if the baby simply rolls off the pad, the alarm may sound.
This monitor offers lots of convenient features. Don’t have the best view of your baby? Use the monitor to remotely pan, tilt or zoom the camera without having to go back into the nursery. Fussy baby? Press a button to play lullabies. Need the camera to move from your bedroom to the nursery? No problem: this freestanding monitor can be set on top of a dresser or grip onto shelves and brackets. You can also unplug it and use it in another room for up to three hours on a single charge. And there’s a room temperature display. But the most impressive feature is its 1,000-foot range—the highest of all cameras on this list. That means you can hear your little one’s every chirp even if you’re hanging out in your backyard.
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