Is there a better way to describe brain activity than EEG "brain waves" I've been reading about EEG brain waves, which are specific waveforms that are observed on the EEG output, and are usually scored by humans. This concept has been around for quite some time.

Is there anything "newer" or "better" than EEG brainwaves discovered in the recent years? 

Given the rise in commercially available EEG sensors, has any company succeeded at putting forth a way to analyze or quantify the output of these sensors to give some useful information to researchers? I'm thinking of brainwave-processing algorithms. For example in Actigraphy, the study of human motion, there are algorithms like "if 19 out of 20 minutes of activity are scored as sleep, then the sleep onset is known to happen at the start of the 20 minute window". Is there something similar for brainwave or derived metrics?
There is no better way to describe brain activity than brain waves! :)

There are newer ways to analyze and think about brain waves, though. Usually you will find these under literature on neuronal oscillations. 

Good aspects of thinking about brain activity using brain waves: 


Brain waves are directly related to neural activity. They are an electric or magnetic measure of current passing through neurons. It doesn't get closer than this (unless you use an invasive technique). In comparison, fMRI measures changes in blood flow over one or two seconds after neurons have fired.
Brain waves are measured essentially at the speed of light, i.e. with no perceptible delay between the onset of neural activity and the moment that the electrode or MEG sensor picks them up. This allows for measuring brain activity as it unfolds, as the brain processes information on the order of milliseconds.


Bad aspects include: 


Seriously compromised spatial resolution. With EEG, the electrical signal gets smeared by passing through the skull. With MEG the measure is more direct, but still, all sensors pick up activity in any part of the brain (at least in EEG; I'm not so sure about MEG), so it is very difficult to say with certainty where precisely something is localized. Methods do exist, but (in my experience) it doesn't come close to MRI precision. It also gets very complicated very quickly.
Activity is picked up only from the neocortex. You can't say much about deep brain activity. 
Brain waves are utterly unintuitive. It is very hard to see how a wavy line on a screen can tell us something about the most interesting thing in the world: ourselves. It is supposed to be related to our consciousness, to our thoughts and feelings, to our personality, state of mind, actions, intentions, everything - yet it's just a wavy line. This is where some hard training in neuroscience comes in.


In the past, brain waves were identified by eyeballing. Nowadays we can do much better. We can imagine that each of these lines is actually composed of many different types of neural activity, happening at different speeds. Neurons firing together quickly will lead to small, brief amplitude changes, whereas neurons firing together at a slower pace will lead to slow waves. The more neurons are firing together, the higher the amplitude of the wave. The faster they are firing together, the lower the wavelength.

The fast and slow wavelengths will be summed up into the single wavy line on the screen, but we can decompose it, e.g. by using a Fourier transform or a wavelet transform. By decomposing, we gain insight into the fact that neurons fire together at different rates when they do different things. For example, if you ignore a visual stimulus, then your visual brain begins to fire at about 10 times per second. This is called the alpha rhythm. If you are actively observing a stimulus, the activity will change to 40-70 times per second. This is the gamma rhythm. Thus, you can say something about what the brain is doing when you see the pattern of neural activity based on a wavy line. 

Also, you might notice that two distant parts of the brain have neurons firing together... but that they are in phase with each other. This might mean that they are both processing different aspects of the same information, so it tells us something about functional neuronal connectivity even though we don't see the underlying white matter firing. 

In any case, brain waves should not really be seen as better or worse than other measures of neural activity. They simply add their bit of information, that is part the larger puzzle of how the brain works. See here for a really nice comparison of M/EEG with fMRI, and a discussion of all the big issues behind noninvasive electrophysiological measures.