Enter a keyword like iPhone in the search box at Twitter.com or get fancy with your search terms for even more precision. Then, click the gear menu next to the search field to save that query for easy access later. (Depending on what version of Twitter.com you're seeing, you might need to follow a slightly different process. If you can't find a gear menu, look below the search field for a button labeled Save This Search. Click this.) Now, when you want to access your saved search, click the search box and it will appear in a drop-down menu. (Or, if you're seeing the old version of Twitter.com, click on the Searches tab near the Timeline tab.) Like the rest of Twitter, saved searches operate almost in real time and will display an alert when new results are available.
Most Twitter clients, including all the ones I've mentioned so far, have long offered various types of advanced data mining like this. As a bonus: if Twitter just isn't your thing but you still want or need to use it for business, you typically don't need an account in most apps to use saved searches.
Get picky with alerts
In times of Twitter Overload, it's good to remember a saying that quickly grew from the service's early days: "You can't read them all." If organizing lists seems like overkill, but you don't want to miss tweets from a handful of accounts, maybe turning on alerts for a chosen few is more your style.
A few apps allow you to receive alerts for tweets from specific accounts, among a slew of other content and services. Appremix's free Boxcar is a good choice across Mac, iPhone, and iPad. Use it to enable Push Notifications on iPhone and iPad for specific accounts. On the Mac, you can install Boxcar's client to display Growl-like alerts. Fabien Penso's $5 Push 4.0 is a competitor focused on iOS devices. It also does Push Notifications.
If all else fails: unfollow
If these other solutions aren't what you're looking for and you really do need to do some serious timeline trimming, there are a bunch of services that can help you make the right decisions. iUnfollow, for example, does exactly what it says on the tin. After logging in with your Twitter credentials, a handful of tools make it easy to find the right people to unfollow (such as users who never followed you back). There are even keyboard shortcuts to ease particularly arduous unfollow sessions.
SocialBro is a sort of "social insight service" that offers a whole range of Twitter analysis tools. Among them is a Follow/Unfollow tool to help you dig into who hasn't followed you back, discover accounts that are just automated bots, and more.
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