Customizing chapter style with tikz

One possibility, using TikZ and the epigraph package; the rounded corner rectangle on top was produced using the pgf library qrr.shapes.openrectangle written by Qrrbrbirlbel in his answer to Tikz shape similar to rectangle with selective drawing of borders (the link to the library can be found in the answer linked):

\documentclass{book}
\usepackage[explicit]{titlesec}
\usepackage{fourier}
\usepackage{tikz}
\usepackage{epigraph}
\usepgflibrary{qrr.shapes.openrectangle}

\definecolor{mybluei}{RGB}{0,173,239}
\definecolor{myblueii}{RGB}{63,200,244}
\definecolor{myblueiii}{RGB}{199,234,253}

\tikzset{
mynode/.style={
  rounded corners=30pt,
  shape=open rectangle,
  open rectangle fill=myblueii,
  open rectangle sides=#1,
  }
}

\titleformat{\chapter}[display]
  {\normalfont\huge\sffamily}
  {}
  {20pt}
  {%
  \begin{tikzpicture}[remember picture,overlay]
  \node[
    anchor=west,
    rectangle,
    minimum height=4cm,
    text width=\paperwidth,
    xshift=-\the\dimexpr\oddsidemargin+1in\relax,
    outer sep=0pt,
    fill=myblueiii] (titlerect) {};
  \node[
    anchor=south west,
    xshift=2cm,
    text width=\textwidth] 
    at ([yshift=5pt]titlerect.south west) {\fontsize{30}{36}\selectfont#1};
  \node[
    mynode=nw,
    anchor=south east,
    fill=myblueii,
    inner xsep=1.5cm,
    outer sep=0pt,
    font=\color{white},
    minimum height=30pt] 
    at (current page.east|-titlerect.north)
     {\bfseries\MakeUppercase{\chaptertitlename}\ \thechapter};
  \end{tikzpicture}%
  }
\titleformat{name=\chapter,numberless}[display]
  {\normalfont\huge\sffamily}
  {}
  {20pt}
  {%
  \begin{tikzpicture}[remember picture,overlay]
  \node[
    anchor=west,
    rectangle,
    minimum height=4cm,
    text width=\paperwidth,
    xshift=-\the\dimexpr\oddsidemargin+1in\relax,
    outer sep=0pt,
    fill=myblueiii] (titlerect) {};
  \node[
    anchor=south west,
    xshift=2cm,
    text width=\textwidth] 
    at (titlerect.south west) {\Huge#1};
  \end{tikzpicture}%
  }
\titlespacing*{\chapter}
  {0pt}{-20pt}{60pt}

\setlength\beforeepigraphskip{1.5\baselineskip}
\setlength\afterepigraphskip{2\baselineskip}
\setlength\epigraphwidth{6.8cm}
\setlength\epigraphrule{0pt}
\renewcommand\epigraphsize{\large}
\renewcommand\textflush{flushright}

\let\oldepigraph\epigraph \renewcommand\epigraph[2]{%
  \oldepigraph{\color{mybluei}\itshape #1}{#2}}


\begin{document}

\chapter{From the Ground Up!}
\epigraph{In theory there is no difference \\ between theory and practice. \\ In practice there is.}{Lawrence ``Yogui'' Berra,1925 \\ New York Yankees baseball player}
\chapter*{A test unnumbered chapter}

\end{document}

'I wrote a tikz code for upper right rounded corner box because i don't want to use

\usepgflibrary{qrr.shapes.openrectangle}

this is my code:

\documentclass{book}

\usepackage{tikz}
\usetikzlibrary{positioning,calc,backgrounds}
\definecolor{mybluei}{RGB}{0,173,239}

\newcommand{\newtab}[2]{%
\begin{tikzpicture}
    \node[inner sep=2mm,text=white] (#1) {#2};
    \begin{scope}[on background layer]
        \draw[fill=mybluei] 
        ($ (#1.north east) $) 
        --($ (#1.north west) $)
        to[out=180,in=90]  ([xshift=-1cm]$(#1.south west) $)
          -- ($ (#1.south east) $)
          -- cycle;
    \end{scope}
\end{tikzpicture}% 
}

\begin{document}
\newtab{test}{CHAPTER 1}
\newtab{test}{This is another test} 
\newtab{test}{This is yet another test}
\end{document}