Scalable database technology and architecture

I've been trying to learn more about database scaling in a distributed system, and I am stuck in between RDBMS and NoSQL.

Some articles online suggest that NoSQL is the solution to modern Big Data. Others say NoSQL is just a hype and RDBMS can be just as scalable with good design, and it provides good data structure.

Instead of reading others' opinions, I'd love to judge the two myself, but I do not understand exactly what is required for a scalable RDBMS and a scalable NoSQL.

I've done a bit more readings on RDBMS, and it seems that the solution requires leveraging memcache and sharding to reduce database size and the number of DB queries. Are there other tricks? Can you still use tables with many columns? Or use less columns and more joins?

As for NoSQL, I've read a little about MongoDB. I understand that it encourages data aggregation. But how does that make it more scalable? I'm also starting to learn Cassandra because I read that it scales much better than MongoDB, but I have no idea how it is more scalable.

I would very much appreciate a basic (or advanced, if you have the patience to type it out) condensed and down-to-the-core explanation on scaling RDBMS and NoSQL, or good articles online or books that explain the topic. :)