How to properly understand Gaussian Units? I have trouble understanding Gaussian Units in relation to SI units: $1/c$ factors seem to appear almost at random, while other constant such as $\varepsilon _0$ or $4\pi$ disappear with seemingly comparable randomness.
The related Wikipedia page is less than helpful, stating things in the manner of: "one difference is that...", "another difference is..." and never giving a full picture on what is going on. How can I convert from SI to Gaussian and back? What is the complete set of rules?
But also.. Why do we bother? I have heard that theoretical physicist prefer to use Gaussian Units over SI units, why is it so? Is it simply a matter of ease of writing?
 A: The SI system has 4 base units: length (m), time (s), mass (kg) and current (ampere).  All mechanical measurements can be expressed as a combination of the 4 base units.  For example, energy $\rightarrow{\rm kg\ m^{-2}\ s^{-2}}$ and  electric charge $\rightarrow {\rm A\ s}$.
The Gaussian system has 3 base units: length (cm), time (s), mass (g). All mechanical measurements can be expressed a combination of these 3 base units. For example, energy $\rightarrow {\rm g\ cm^{-2}\ s^{-2}}$, electric charge $\rightarrow {\rm g^{1\over 2}\ cm^{3\over 2}\ s^{-1}}$ and current $\rightarrow {\rm g^{1\over 2}\ cm^{3\over 2}\ s^{-2}}$.
Note the awkwardness of the base unit ampere in the SI system. This is one of the reason why physicists prefer the Gaussian system while engineers prefer the SI system.
How the SI System Came About
When experimentalists observed that currents in two parallel wires can produce a force, they decided to define a new base unit, the ampere ($\rm A$), to quantify currents. In the SI system,  1 $\rm A$ is defined as the constant current between two parallel wires spaced 1 $\rm m$ apart that produces $2 \times 10^{-7 } {\rm N}$ of force per unit length.
Consequently, one can define the electric charge (Coulomb) as current $\times$ time. In the SI system, 1 Coulomb is defined as the quantity of electric charge carried in 1 $\rm s$ by a current of $1$ A.
The electric charge defined this way forces us to write Coulomb's law $\vec{F}=k\frac{q_1 q_2}{r^2}$ as $$\vec{F}=\frac{1}{4\pi\epsilon_0}\frac{q_1 q_2}{r^2},$$ where the constant of proportionality $k$ is fixed to be equal to $\frac{1}{4\pi\epsilon_0}$.
So, in this system, we needed a new base unit to define currents. Also, we can't talk about electric charge without referring to currents. Is there a better way to do this?
Why the Gaussian System is Better
In the Gaussian system, the electric charge is defined directly using Coulomb's law $$\vec{F}=k\frac{q_1 q_2}{r^2},$$  where the constant $k$ is picked to be equal to 1. One statcoulomb  is defined as the charge carried by two stationary objects 1 $\rm cm$ apart that produces a force of 1 dyne (i.e. 1 $\rm g\ cm\  s^{-2}$).
The current is then naturally defined as the quantity of charge that flows through a point per unit time. There is no need to define a fourth base unit just to measure current.
Compared to the SI system, the Gaussian system is defined in a simpler and more elegant way. No wonder theoreticians like it more!
PS: Another reason why the Gaussian system is better is that the electric and magnetic fields have the same units. This is nice since electric and magnetic fields transform into each other under Lorentz transformations.
A: To your question as to "why do we bother" here is a comment by Val Fitch [1] (https://en.wikipedia.org/wiki/Val_Logsdon_Fitch) on the same subject:

Many thanks for your editorial comments on units @Robert H. Romer,
‘‘Units: SI-Only, or Multicultural Diversity?’’ Am. J. Phys. 67(1),
13–16 (1999). As you imply, units are a cultural matter—not
scientific. And, as you stopped just short of saying, any system that
gives E and B different units, when they are related through a
relativistic transformation, is on the far side of sanity.

[1] Fitch: "THE FAR SIDE OF SANITY", Am. J. Phys., Vol. 67, No. 6, June 1999, p467
A: You may want to look at the answer that I posted here. In a nutshell: choosing a system of units is a matter of convenience, and different fields of science and engineering use different units (including different systems used in different domains of theoretical physics).
