Question: What's the difference between `.bashrc` and `.bash_profile` and which one should I use?

Answer: 
Traditionally, when you log into a Unix system, the system would start one program for you. That program is a shell, i.e., a program designed to start other programs. It's a command line shell: you start another program by typing its name. The default shell, a Bourne shell, reads commands from `~/.profile` when it is invoked as the login shell.

Bash is a Bourne-like shell. It reads commands from `~/.bash_profile` when it is invoked as the login shell, and if that file doesn't exist¹, it tries reading `~/.profile` instead.

You can invoke a shell directly at any time, for example by launching a terminal emulator inside a GUI environment. If the shell is not a login shell, it doesn't read `~/.profile`. When you start bash as an interactive shell (i.e., not to run a script), it reads `~/.bashrc` (except when invoked as a login shell, then it only reads `~/.bash_profile` or `~/.profile`.

Therefore:

* `~/.profile` is the place to put stuff that applies to your whole session, such as programs that you want to start when you log in (but not graphical programs, they go into a different file), and environment variable definitions.
* `~/.bashrc` is the place to put stuff that applies only to bash itself, such as alias and function definitions, shell options, and prompt settings. (You could also put key bindings there, but for bash they normally go into `~/.inputrc`.)
* `~/.bash_profile` can be used instead of `~/.profile`, but it is read by bash only, not by any other shell. (This is mostly a concern if you want your initialization files to work on multiple machines and your login shell isn't bash on all of them.) This is a logical place to include `~/.bashrc` if the shell is interactive. I recommend the following contents in `~/.bash_profile`:

```
if [ -r ~/.profile ]; then . ~/.profile; fi
case "$-" in *i*) if [ -r ~/.bashrc ]; then . ~/.bashrc; fi;; esac

```

On modern unices, there's an added complication related to `~/.profile`. If you log in in a graphical environment (that is, if the program where you type your password is running in graphics mode), you don't automatically get a login shell that reads `~/.profile`. Depending on the graphical login program, on the window manager or desktop environment you run afterwards, and on how your distribution configured these programs, your `~/.profile` may or may not be read. If it's not, there's usually another place where you can define environment variables and programs to launch when you log in, but there is unfortunately no standard location.

Note that you may see here and there recommendations to either put environment variable definitions in `~/.bashrc` or always launch login shells in terminals. Both are bad ideas. The most common problem with either of these ideas is that your environment variables will only be set in programs launched via the terminal, not in programs started directly with an icon or menu or keyboard shortcut.

¹  For completeness, by request: if `.bash_profile` doesn't exist, bash also tries `.bash_login` before falling back to `.profile`. Feel free to forget it exists.
The configuration logic of bash's itself is not crazy complicated and explained in other answers in this page, on serverfault and in many blogs. The problem however is *what the Linux distributions make of bash*, I mean the complex and various ways they configure bash by default. <http://mywiki.wooledge.org/DotFiles> mentions some of these quirks briefly. Here's one sample trace on Fedora 29, it shows which files source which other file(s) and in which order for a very simple scenario: remotely connecting with ssh and then starting another subshell:

```
ssh fedora29
 └─ -bash # login shell
      ├── /etc/profile
      |    ├─ /etc/profile.d/*.sh
      |    ├─ /etc/profile.d/sh.local
      |    └─ /etc/bashrc
      ├── ~/.bash_profile
      |    └─ ~/.bashrc
      |          └─ /etc/bashrc
      |
      |
      └─ $ bash  # non-login shell
            └─ ~/.bashrc
                 └─ /etc/bashrc
                       └─ /etc/profile.d/*.sh

```

Fedora's most complex logic is in `/etc/bashrc`. As seen above `/etc/bashrc` is a file bash itself doesn't know about, I mean not directly. Fedora's `/etc/bashrc` tests whether:

* it's being sourced by a login shell,
* it's being sourced by an interactive shell,
* it has already been sourced

... and then does completely different things depending on those.

If you think can remember the graph above then too bad because it's not nearly enough: this graph merely describes just one scenario, slightly different things happen when running non-interactive scripts or starting a graphical session. I've omitted `~/.profile`. I've omitted `bash_completion` scripts. For backward compatibility reasons, invoking bash as `/bin/sh` instead of `/bin/bash` changes its behaviour. What about zsh and other shells? And of course different Linux distributions do things differently, for instance *Debian and Ubuntu come with a non-standard version of bas*h, it has Debian-specific customization(s). It notably looks for an unusual file: `/etc/bash.bashrc`. Even if you stick to a single Linux distribution it probably evolves over time. Wait: we haven't even touched macOS, FreeBSD,... Finally, let's have a thought for users stuck with the even more creative ways their admins have configured the system they have to use.

As the never-ending stream of discussions on this topic demonstrates, it's a lost cause. As long as you just want to add new values, some "trial and error" tends to be enough. The real fun begins when you want to *modify* in one (user) file something already defined in another (in /etc). Then be prepared to spend some time engineering a solution that will never be portable.

For a last bit of fun here's the "source graph" for the same, simple scenario on Clear Linux as of June 2019:

```
ssh clearlinux
 └─ -bash # login shell
      ├── /usr/share/defaults/etc/profile
      |    ├─ /usr/share/defaults/etc/profile.d/*
      |    ├─ /etc/profile.d/*
      |    └─ /etc/profile
      ├── ~/.bash_profile
      |
      |
      └─  $ bash   # non-login shell
           ├─ /usr/share/defaults/etc/bash.bashrc
           |      ├─ /usr/share/defaults/etc/profile
           |      |    ├─ /usr/share/defaults/etc/profile.d/*
           |      |    ├─ /etc/profile.d/*
           |      |    └─ /etc/profile
           |      └─ /etc/profile
           └─ ~/.bashrc

```