How are electronic gadgets made slimmer and compact? OR How are more features added without increasing gadget size?

Edit: 4 Feb 2016 - I got a lot of feedback about this post and many told me it looks rushed. My answer is, that is exactly how I want it to be. If I go into the core technicalities, it will become tiresome for my blog followers from a field other than Electronics. I however, really appreciate the feedback and have added some links to deeper information at the end. Thank you everyone!   

About 80% of what is written here springs from a subject, 'IC Technology' taught in my 7th Sem of Engineering.
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"How do they reduce the thickness of our smart-phones and make the circuit size smaller?" 

"How come they are offering 128GB of storage in that small micro-SD memory card!?"

I get these questions a lot!

To all of you curious people, I now consider myself qualified enough to answer this and this itself is my career choice! :)
The answer is : Very Large Scale Integration(VLSI) and Moore's Law and we will further discuss it in this post. Hope you enjoy this crash course! :)

VLSI

I am taking you to Semester 3 and 5 of my Engineering. What I am about to talk on is the most basic building block of any circuit(memory cards, processors etc.), that is, a 'Transistor'.
Bottom line: Smaller the transistor, more dense is the circuit or more features can be made available in previous integrated circuit, keeping size same.

This is how more space is made available in memory card without increasing its size! Smaller transistors occupy less space and hence more transistors are fitted to give more data storage capacity.

Details:
Lets say you have a transistor. Specifically a type of transistor called as a MOSFET(Metal-Oxide Semiconductor Field Effect Transistor). MOSFET sounds pretty complex but, for our present scope, lets say it is as simple as pushing a button to switch ON/OFF a light.

Basic diagram of all MOSFETs at the core level: Made using a material called Silicon, its other types and its oxides. 

The ones we use for our experiments in college, have dimensions in centimeters like these:

In the transistor package featured above, a billion transistors can be fitted, in place of just one. However, the package is made purposely bigger, just so that we can handle it. Otherwise even this bigger transistor has a smaller circuit inside, like shown in the diagram. 

To explain the scale we are talking about, in size reduction using VLSI, Apple's A8 processor introduced in the iPhone 6 has a size of 1.05cm x 0.85cm and has 2 Billion transistors. That's VLSI. Each transistor on this chip has dimensions in nano-meters.

This is how an extremely small size transistor fabricated at the nano-meter scale looks like:

This is a special type of transistor, called a FinFET.

They have special laboratories to fabricate components on the nano-scale. They are called nano Fabrication Laboratories or FabLabs. Here is a view of one:

Companies like IBM and Intel came up with transistors which are even smaller(9 nm). They use something called as Carbon Nano-Tubes(CNT) Technology.

Carbon allotropes like Graphene (a single layer sheet of carbon with a thickness of 1 atom) are unleashing a completely new era of electronics! CNT is made by rolling up this Graphene sheet. We will soon have (and already have) technologies like fold-able and roll-able screens, transparent electronic gadgets and micro-circuits which can be extremely useful in bio-medical and wireless applications!

Processors and gadgets's circuits are thus becoming smaller, energy efficient and even more powerful! Now-a-days Systems-on-Chip or SoC are gaining more popularity. The processors in our phones are not just processors or CPU, they are an SoC. SoC means they can do the mathematical processing, as well as the graphical processing and have on-chip memory which makes them blazing fast!

Example: Apple iPhone SoCs

Moore's Law

The co-founder of Intel and Fairchild Semiconductor, Gordon E. Moore postulated that the number of transistors in a dense integrated circuit will double every two years. This postulate became such a common phenomenon that we now call it a law!

For example: A 4 TB external HDD of 2014 is of same size/smaller than 2 TB HDD of 2012. See how the transistors doubled in the same space! :)

Brace yourselves. 'The Future' is no longer the future..its already happened! =) 

Links to more info:
Semiconductor device fabrication - Wikipedia
VLSI Fabrication Technologies - Emanuele Baravelli
VLSI Design, Fabrication steps and layout - Shaahin Hessabi
IC Fabrication Techniques - circuitstoday.com