Some previews don’t work, so I tested them on a side blog with random posts on it. You should do the same.

1 COLUMN (WITH AND W/O SIDEBAR)

REDUX

NEOPIAN 

PLAIN

BS by howblank

BLANCO by iwriterudewords

ASTERISM

SIMPLEMINDED

DRIFTER

GRAMPAW

PLANEJANE

DEAD SIMPLE by amwelles

DOWNPOUR by valhallaisland

BLEEDING by the-underlings 

STEAMBLR by theloudestsongs

MONO by ferbivore

MONOSPACE by unused-blog-i-guess

PURE BLACK 156L 

FLASHBACK TO SIMPLICITY by drevlyanin-blog

CODE&SPACE by noahdoersing 

MINIMAL MONO by nathanwentworth

SPIRIT by saltchip

2001 by samuel-fine-blog

VIEWPORT

LEFTY 

MIDDLEAGE

STIRRED by cubicle17

PORTFOLIO - FOCUS PHOTOGRAPHY by balconythemes

MERV by venidro  

FOUDRE by eggdesign

TIME CAPSULE by petervidani

OEPIDA MAAS by paulhabeeb

PLAIN TIMES by paulhabeeb

ATLAS by evanwalsh

X-RAY by nonspace​

ECLYPS by bpdylan89

THE FIX by romandavid

UNKNOWING

CLEAR

A PERSONAL BLOG by designblogworld

LITE by shikadi

TYPEWRITER by erichu

WRITTEN by projectorthemes-blog

SIMPLY RHYTHM by sydneyzh

TEMPORAL by bisexual-archer

LEER by Renz Abong

SAWANO by kwanfushing

THEME #000000  

OG by mayhopar

BLUE OASIS by longwake

GRIDULAR by lethallywaken

TERMINAL by fuyei-blog1

NEOTERMINAL by thefizzynator

TERMINAL FLASHBACK by ninjineer

DARK NEON TUMBLR THEME by crxnagorgon

APOLLO by sanographix-theme

2993 by behradghadiri 

LIMES by lornings

A BIT DIFFERENT by axialthemes

GARDEN by axialthemes

CHROMOSPHERE by cubeghost

PULSAR  by cubeghost

THE THEME by lutzpreuss

THE ONE  by lutzpreuss

EINFACH by einfach-theme

CAEZA’ E’ PERRO 

BLACK BEAUTY by thisisoverforayears-blog

PERSISTENCE by norojilives

 NATUREX by norahfields

LITEWEIGHT. by elleusine

GLOW. by elleusine

EXPORT by 1c3-c0ld-blog

THEMOPOLIS by anthagio

NIGHTNIGHT by blk--boi

FLOATING THOUGHTS by losstopschade

BANNER

FUTURISMO by sottsass

ELEGANT BOX

BIT by level82-blog

INSP

START FROM THE END by go-crazy

OPTIMIZED

CONTINUUM

2 COLUMNS

RAW by howblank

ASHEN by neutral 

VIVIANACKS by norahfields

DUAL by askfuse

GRID

STYLD by webcodeine

MOONLIGHT by azurih

PORTFOLIO - HELKA by balconythemes

PATION by zenhance 

MELVIN by zenhance

ACME by grffnco

HIKARI by kwanfushing

MIDORI by kwanfushing

HAROLD by glitter-themes

TIGORA by bajuzzz

CLUDS  by bajuzzz

IMAGE FOLDER by minhhung

DIVERSE by desparate

FULL SIZE (WIDE POSTS)

UNCOOKED by jonaspelzer

PORFOLIO-THEME-FOR-MAIN-BLOG by balconythemes 

NOUR by thesethemes 

MINISHIO by shiotest-blog 

MMMMINIMAL by rainerbird

BROOKLYN

PRESET by themeset

LAYOUT THEME by tomsansome

CHROME PDF VIEWER by tomsansome

MINIM THEME by certifiction

KEEP IT SIMPLE.

THE DEFAULT NETWORK 3.1 by markboyce

CONTAINER

WOZ by itssortastupid

Tumblr's Theme Editor uses HTML5, though you can use JSON to display your posts (specially & recommendably if you're using the Neue Post Format or 'NPF' which, when you find about, you won't like one bit as the majority of us) or AJAX to load your post notes.

You have a Resource Manager for theme-related resources at your disposition. You can upload your media or external styles & scripts here and Tumblr will provide a unique url for each, which you can later paste to link as the tags' source.

Read this Theme Documentation that shows most –but not all though– of Tumblr's variables, which are basically shorthands that get replaced for their final references on the live code.

Almost all HTML tags are allowed: space elements <header> <section> <main> <arcticle> <footer> <div> (of course), headings <h1>, <h2>...<hN>, icons, figures, images, iframes, links, hyperlinks, ordered or unordered lists, and even your own custom meta-tags for prebrowsing, opengraphs and schema. You can of course use your own custom classes and ID's for the mentioned tags for further CSS style customization.

Speak of Style, you can use inline, embedded or linked styles on your Tumblr theme. You don't have to embed all your styles: you can link external stylesheets using the Resource Manager or another hosting service such as Dropbox.

All media queries are compatible and customizable for web responsiveness, and you can use as many as you want/need, both on internal and external CSS. Additionally, media queries can be nested within one another (yes, even in basic CSS, no preprocessor needed).

Tumblr uses CSS3 for inline or embedded styles in the Editor, yet –I think, haven't tested– is compatible with syntactical and some other popular style preprocessors like SCSS or SASS (for external styles only) if you want/need your styles nested.

Similarly, Tumblr accepts vanilla JavaScript for embedded script writing, but you can link external libraries such as jQuery and AJAX. You'll notice, though, hypertext preprocessors (or PHP) are not allowed; so, even if you can add and style your own contact form or other input tags, you won't be able to connect those to a .php action document even if it's hosted in another host service and, hence, to make it functional. This is mostly for security reasons as far as I've understood.

We are allowed to add hyperlinks to external services (such as Facebook, Instagram, Spotify...) to mimic a Social action bar, though from now on they must all be compatible with HTTPS security protocol or either Tumblr won't redirect anymore. We are allowed as well to embed custom and external iframes (like, for example, a YouTube video or a custom widget).

You can choose your theme's typography from among over 20 free fonts available at Tumblr's editor by default. If none of those fully catch your eye, you can upload your own custom font files (only .woff webfonts though) to the Resource Manager to use them as font families, or even link as many fonts as you like from Google Fonts or other public font libraries.

If you've accidentally deleted your theme or erased part of your code, you can easily recover an automatically-saved backup at Tumblr's Theme Recovery page. Though be careful, for you've got access only up to 20 backup copies, so avoid overuse of the 'Save' button or else your theme's oldest versions will be gone forever.

Just in case you're wondering, you ain't forced to share your custom theme publicly with the comunity. However, know that you could –if you want to– publish your theme at the Theme Garden for everyone else to install and use, either paid or for free. You also ain't forced to use all the variables from the theme documentation; but know that if you aim to make your theme public, you have to cover the basic ones and follow these guidelines for theme sharing and it will be pending for approval by the Team.

Some other technologies compatible with Tumblr:

Flexbox

CSS Grid

OpenGraph

Webkit Tools

Pseudoclasses

CSS basic animations

Google Fonts, Font Awesome and other font libraries